Problem Solving

 

A daily problem solving activity (problem) is posted on our daily bulletin.  These may or may not align with Algebra standards, they may or may not involve mathematical computations, and they may or may not require super analytical ability.  Hopefully students will expand their problem solving ability through this daily exercise.   And hopefully our Math scores will increase due their use.

Many have been copied from openly available examples on the internet.  Some have been lifted from printed texts.  Names and numbers could have been altered to protect the innocent, or they have been inserted to generate interest.  Good luck in solving all the daily problems!!

1.      The cost of a cab ride with the Austin Eagle Taxi Company has an initial cost of $2.50 plus $0.15 for each ¼ mile.  Which expression can be used to calculate the cost of a cab ride that is d miles long?

A.     (2.50 + 0.15)d

B.     (2.50 + 0.60)d

C.     0.15d + 2.50

D.     0.60d + 2.50

 

2.      Mr. Plasse went on a 152-mile bicycle trip.  During the first 3 hours, he traveled a total of 57 miles.  If he maintained this speed for the remainder of the trip, what was the total time, in hours, of his trip?

A.     6 hours

B.     7 hours

C.     8 hours

D.     9 hours

 

3.      For the equation 5y = 3x + 10, what is the value of x when y = 0?

A.     -3 1/3

B.     3/10

C.     -2

D.     2

 

4.      Which of the following inequalities represents the statement, “Seventy decreased by three times a number, x, is greater than forty”?

A.     3x – 40 > 70

B.     70 – 3x > 40

C.     70 + 3x > 40

D.     40 – 3x > 70

 

5.      Three miles per minute is the same rate as which of the following?

A.     10 miles per second

B.     180 miles per hour

C.     60 miles per hour

D.     20 miles per second

 

6.      At her part-time job, Carmen first made $9.50 an hour.  After her supervisor gave her a raise, she made $10.26 an hour.  By what percentage did her wage increase?

A.     8%

B.     9.5%

C.     10.3%

D.     11%

 

7.      A full water cistern holds 220 gallons of water.  Water leaks our at a rate of 1.2 gallons per hour.  How much water remained in the cistern if it was full 24 hours ago?

A.     28.8

B.     191.2

C.     196

D.     208

 

8.      What is the next term in the sequence 1, 2, 3, 5, 8, 13, ___

 

A.     21

B.     20

C.     18

D.     14

 

9.      Evaluate (16 – 4) ÷ 12 x 15

 

A.     1 1/3

B.     1

C.     1/15

D.     15

 

10.  Simplify 6a + 15a

 

A.     6a + 15a

B.     21a2

C.     42a

D.     21a

 

11.  Simplify 3 + 2(xy + 3z) + 4xy

 

A.     6xy + 6z + 3

B.     9xy + 15z

C.     6xy + 3z + 3

D.     5xy + 3z + 3

 

12.  Evaluate 52

 

A.     10

B.     25

C.     30

D.     32

 

13.  Write 3/5, 6/15, and 13/30 in order from the least to the greatest.

 

A.     3/5, 6/15, 13/30

B.     6/15, 13/30, 3/5

C.     6/15, 3/5, 13/30

D.     13/30, 6/15, 3/5

 

14.  Which makes the sentence ¾ ___5/16 true?

 

A.     =

B.     >

C.     <

D.     None of the above.

 

15.  Simplify  -6a + (-12a)

 

A.     18a

B.     6a

C.     -18a

D.     -6a

 

16.  Translate “two times a number is six times the sum of z and y” into an equation, inequality, or formula.

 

A.     2x = 6 (zy)

B.     2 + x = 6 + z + y

C.     2x = 6(z + y)

D.     2x = 6z + y

 

 

17.  What is the slope of a line parallel to the line -9x + 5y = 11?

A.     -9/5

B.     -5/9

C.     5/9

D.     9/5

 

18.  If c = -3 and d = 5, then 4c(d – 7) Squared =?

A.     48

B.     24

C.     -24

D.     -48

 

19.  Parking fees for the DuRite Parking Garage are listed below:

Up to 30 minutes – Free

31 minutes to 1 hour - $5.00

61 minutes to 3 hours - $7.00

Over 3 hours - $7.00 plus $0.75 per hour or fraction of an hour.

            Mr. Herald parks at this garage for 6 hours and Ms. McNew parks at this garage for 1.5 hours.  How much more money will Mr. Herald pay than Ms. McNew?

A.     $2.00

B.     $2.50

C.     $3.00

D.     $4.50

20.  Simplify:  9 – 5 – (-2)

A.     2

B.     6

C.     8

D.     12

 

21.  Jake works in a factory where he earns $9.50 per hour, up to 35 hours.  For each hour beyond 35 hours, he earns 1.5 times his hourly pay.  Which expression can be used to determine Jake’s income for a week in which he works x hours?  Assume that x is greater than 35.

A.     (9.5)(35) + (1.5)(9.5)(x-35)

B.     (9.5)(35) + 14.25x

C.     (9.5)(x-35) + 14.25x

D.     (1.5)(9.5)x

 

22.  One pound is approximately 0.453 kilogram.  Pete weighs 150 pounds.  What is his weight to the nearest kilogram?

A.     45 kg

B.     68 kg

C.     150kg

D.     331 kg

 

 

23.  The side of a square is n centimeter long.  The area of the square is 9 square centimeters.  Which equation can be used to find the length of the square?

A.     n2 = 3

B.     n2 = 9

C.     n2 = 18

D.     n2 = 9

 

24.  Simplify:  -9 – (-6) + 7 + (-4)

A.     6

B.     8

C.     0

D.     -8

 

25.  If a sports league has, t,  teams and each team plays all the other teams twice, the total number of league games, g, is given by this function:    g = t2 – t         The High Plains Softball League plays a total of 72 games, with all teams playing each other twice.  How many teams are in the league?

A.     7

B.     8

C.     9

D.     10

 

26.  The odometer on Ms. Fraley’s car just before she began a trip read 20,416 miles.  After 3 hours of traveling, the odometer read 20,602 miles.  Which equation can be used to find r, Ms. Fraley’s average rate of speed for 3 hours?

A.     r = 20,602 – 20,416

         3

B.     r = 20,602 – 20,416

 

C.     r = 3 (20,602 – 20,416)

 

D.     r – 20,602 – 20,416

3

 

27.  Simplify:  6x – 6 + 9 + 5x -7

A.     11x – 10

B.     10x – 8

C.     11x – 4

D.     10x - 9

 

28.  Mr. Watt’s history grade will be determined by the average of 4 tests.  He received a 76, an 85, and a 74 on the first 3 tests.  He needs to get an average of at least 80 to receive a B.  Which inequality can be used to find g, the minimum grade Mr. Watts must make on the fourth test to receive a B in history?

A.     76 + 85 + 74 + g

4                      ≥     80       

 

B.     76 + 85 + 74 + g

                   3                     ≥     80      

 

C.     76 + 85 + 74 – g

4                      ≥     80

 

29.  The area of a triangle is given by the equation:  h2 – 6h = 72 , where h is the height of the triangle.  What is the value of h?

A.      9

B.     12

C.     24

 

30.  Simplify:  1 + (n – 9) + 6n

A.     7n – 8

B.     7n – 10

C.     5n – 9

D.     5n + 8

 

31.  The owner of a bookstore recorded the following information from a recent week.  

Number of  Customers             Amount of Sales

12                                                           $80

18                                                           $110

24                                                           $140

30                                                           $170

36                                                           $200

42                                                           $230

According to information in the table, which equation describes the relationship between the number of customers and the amount of sales?

A.     s = 6c + 30

B.     s = c + 30

C.     s = 5c + 20

D.     s = c + 30

    6

 

32.  These are a set of values for x and y: 

x    -2         -1         1          3          4

y    -7         -4         2          8          11

 

Which equation best represents this set of data?

A.     y = x – 5

B.     y = x + 3

C.     y = 3x -1

D.     y = -x -5

 

33.  Simplify:  8a3 + 6a3 + 11a – 3a

A.     14a6 + 8

B.     14a3 + 8a

C.     14a3 + 8

D.     14a6 + 8a

 

34.  The local video store charges $10 per year for membership and $3 per day for movie rentals.  If x stands for the number of rentals Mr. Barrett rents in a year, which expression can be used to find the amount he pays in a year?

A.       3 ( x + 10)

B.     10x + 3

C.     3x + 10

 

35.  Mr. Haven has a 72-gram sample of a radioactive substance.  This substance decays into a non-radioactive compound.   Mr. Haven monitored the sample every 10 hours to determine how much radioactive material remained. 

 

Radioactive Decay                                            How many grams of radioactive material

Time (hours)--  Mass (grams)                           would be expected at 50 hours?

0          --         72

10        --         36                                                        A.  1 g

20        --         18                                                        B.  2.25 g

30        --         9                                                          C.  3 g

40        --                                                                     D.  4.5g

50        --

 

36.  Which binomial is equal to:   x2 + 3x – 6 + 4x2 – 2x + 6 ?

            A.  4x4 + x2

            B.  5x4 + 1

            C.  5x2 + 12

            D.  5x2 + x

 

37.  A sample of 247 cd’s had 2 defective disks.  At this rate, approximately how many defective disks will be found in 10,000 disks.

           

A.  500

            B.  40

            C.  8

            D.  80

 

38.  The longer leg of a right triangle is 3 inches longer than x, the length of the shorter leg.  The hypotenuse is 15 inches long.  This equation shows the relationship between the sides:     x2 + (x + 3)2 = 225     What is the length of the shorter leg?

           

A.  6 in

            B.  9 in

            C.  12 in

            D.  18 in

 

39.  Which trinomial is equal to:  9a2 – 7a + 1 – 2a2 – 5a + 13 ?

            A.  7a2 + 12a + 14

            B.  7a2 – 12a + 14

            C.  2a2 + 7a + 14

            D.  5a2 – 2a + 14

 

 

40.   In Louisville, 70% of the taxicabs are yellow and 20% have air conditioning.  If the cabs are randomly scattered across Louisville, what is the probability a cab picking you up is a yellow cab with air conditioning?

 

A.  14 of 100

B.  9 of 100

C.  90 of 100

D.  5 of 100

 

41.  The ratio of the lengths of three sides of a triangle is 4:6:8.  The perimeter of the triangle is 72 inches.  The length of the shortest side of the triangle is:

 

A.     18 inches

B.     4 inches

C.     32 inches

D.     16 inches

 

42.  Which of the following could be the next step in solving the equation:                                                             

-2 (x + 4) = 1 + (3 – x)

 

A.     -2x + 8 = 1 + 3 – x

B.     -2x – 8 = 1 + 3 + x

C.     -2x + 4 = 1 + 3 – x

D.     -2x – 8 = 1 + 3 – x

 

43.  Mr. Carter bought iced tea for $1.05, wings for $3.45, 3 cookies for $.75 each and paid 5% sales tax.  What was his change from $20.00?

 

A.     $12.91

B.     $13.41

C.     $13.96

D.     $14.41

 

44.  Write the following expression with exponents.

b x b x b x b x b x b x b x b x b

 

A.     b18

B.     9b

C.     b2

D.     b9

 

 

45.  Mrs. Sterk wants to put a sidewalk around a rectangular garden.  The garden is 7 feet wide and 18 feet long.    The area of the garden would then be a = 7 x 18.  The sidewalk will be the same width all the way around the garden   (2x + 18) (2x + 7).

If the area of the sidewalk is 150 square feet, how wide is it?

 

A.     2.5 ft

B.     3.5 ft

C.     5 ft

D.     5.5 ft

 

  1. Simplify:  4 (7z – 4) – 5 (3a – 6)
    1. 3a – 5
    2. 6a + 22
    3. 12a – 11
    4. 13a + 14

 

  1. To convert a temperature in degrees Fahrenheit, F, to a temperature in degrees Celsius, C, the following formula can be used.
    1. C = 5/9 (F – 32)

 

What is the minimum value of F that will make C greater than or equal to 70?

 

a.       68.4

b.      94

c.       126

d.      158

 

  1. Mr. Hougland earns $650 per month plus an 8% commission on his sales.  If he sold x dollars of merchandise last month, which equation can be used to find y, his total earnings last month?        
    1. y = x + .08x
    2. y = (650 + .08)x
    3. y = .08 (650 + x)
    4. y = 650 + .08x

 

  1. Simplify:  3x (6x + 2) – 5x (x – 7y) – 3 (2x + 5y)
    1. 13x2 + 35xy – 15y
    2. 13x2 + 25xy – 15
    3. 13x + 35xy – 15y
    4. 13x2 + 18xy – 6y

 

  1. Mr. Stuckwish bought the following items at the store.
    1. 1 gal milk                      $2.17
    2. 2 lb hamburger $3.98
    3. 3 donuts                       $ . 99
    4. tube toothpaste $2.79
    5. 1 pair socks                  $1.57

He paid 6% sales tax.  What was the total cost of his purchases?

a.       $11.50

b.      $11.70

c.       $12.19

d.      $13.65

 

  1. Mr. Ahlbrand made a circular flower garden that is 3 feet in diameter.  He wants to buy edging that will keep grass from growing in the flowers.  How many feet of edging will he need to buy to go around the outside of the flower garden? 
    1. 4.71 feet
    2. 6.00 feet
    3. 9.42 feet
    4. 18.84 feet

 

  1. Simplify:  -10 (6a -7) + 5 (5a + 2)
    1. -35a + 80
    2. -85a - 7
    3. 6a – 17
    4. -35a - 60

 

  1. Concession stand sales for each game in the season were $320, $540, $230, $450, $280, and $580.  What is the mean (average) sales per game?
    1. $230
    2. $350
    3. $385
    4. $400

 

  1. Taco Belle restaurant uses 18 pounds of Monterey Jack cheese every day.  The restaurant is open 7 days a week.  The restaurant orders the cheese in 10 pound blocks.  How many 10 pound blocks of cheese should the cooks order each week to have enough?
    1. 2
    2. 10
    3. 13
    4. 126

 

  1. What is the Greatest Common Factor of :  27ab4 and 45a2b3   ?

a.       3ab3

b.        9ab3

c.         3a2b4

d.        9a2b4

 

  1. On a blueprint of a house, the scale is 0.25 inches equals 2 feet.  How wide is the kitchen if it measures 1.5 inches on the blueprint?
    1. 0.33 feet          
    2. 3 feet
    3. 12 feet
    4. 15 feet

 

  1. Mrs. Daniel wanted to divide 7.86 by 3.9, but forgot to enter the decimal points when she put the numbers into the calculator.  Using estimation, where should Mrs. Daniel put the decimal point?
    1. 0.2015
    2. 2.0153
    3. 20.153
    4. 201.53

 

  1. Factor:  49a6 – 28a3
    1. 7a3 (7a3 – 4)
    2. 7a3 (7a3 – 4a)
    3. 7a3 (7a2 – 4)
    4. 7a6 (7a – 4)

 

  1. Carl, Kayla, Sean, Pete, Amanda, and Billy form a circle.  Sean is beside Amanda, and Amanda I beside Kayla.  Pete is between Carl and Kayla.  Who is Billy between?
    1. Kayla and Amanda
    2. Sean and Amanda
    3. Pete and Carl  
    4. Carl and Sean

 

  1. Mr. White is three years older than twice his brother’s age, b.  Which algebraic expression below represents Mr. White’s age?
    1. b + 3
    2. 2b + 3
    3. 3 – 2b
    4. 2b – 3

 

  1. Multiply:  (x + 6) (x + 3)
    1. X2 + 9x + 9
    2. X2 + 9x + 18
    3. 2x2 + 9x + 18
    4. 2x2 + 6x + 9

 

  1. It takes 1 2/3 yards of fabric to cover one chair.  If Mrs. Sturgeon bought 12 yards of fabric, how many yards would she have left if she covered 6 chairs?
    1. 2 yards
    2. 4 1/3 yards
    3. 6 2/3 yards
    4. 10 yards

 

63.  The area of a rectangle is given by the equation:  2x2 = 450    where x is the width of the rectangle.  What is the width?

           

A.  5

            B.  9

            C.  15

            D.  25

 

  1.  Mrs. Conner has budgeted $6500 for a computer lab.  Each new computer costs $750, and each new computer table costs $60.  If Mr. Gibson buys 8 new computers, which inequality can be used to find t, the number of new tables he can buy?

 

    1. 8 (750 + 60)t ≤ 6500
    2. 8 (750t) = 60 ≤ 6500
    3. 750 = 60t ≤ 6500
    4. 8 (750) = 60t ≤ 6500

 

  1. Multiply:  (9n + 2) (n – 4)
    1. 9n2 – 34 – 8
    2. 9n2 – 34n – 2
    3. 10n2 – 34n – 2
    4. 10n2 – 7n - 8

 

  1. The number of pieces of mail processed by a machine in the post office is directly proportional to the number of minutes the machine runs.  The machine processes 2700 pieces of mail in 60 minutes of continuous running.  How many pieces of mail would the machine process in 25 minutes of continuous running?
    1. 108
    2. 675
    3. 900
    4. 1125

 

  1. Mrs. Turner has $264 in her bank account.  She needs to deposit enough money to make his car payment of $189 and still have at least $150 left in his account.  Which inequality describes d, the amount of money Mrs. Turner needs to deposit?
    1. d (264 – 189) ≥ 150
    2. 264 – 189 + d ≥ 150
    3. 264 – 189d ≥ 150
    4. d – 189 ≥ 150

 

  1. If x = n3, which expression is equal to n12?
    1. x3
    2. x4
    3. x7
    4. x9

 

69.  What is the value of x in the following equation?   3x – 4(x+1) + 10 = 0

            A.  2

            B.  6

            C.  10

            D.  11

 

  1.  The circumference of a circular rug is about 31.4 feet, and its aea is about 78.5 square feet.  What is the approximate radius of the rug?
    1. 5 ft.
    2. 7 ft.
    3. 9 ft.
    4. 10 ft.

 

  1. Mrs. Ostertag wants to put a fence around a corner of her property.  She has 320 feet of fencing and plans to use at least one-half of it.  The fenced are will be shaped like a right triangle with sides in the ratio of 3:4:5.  Which range describes the length of the shortest side of the triangle?
    1. Less than 40 ft
    2. From 40 ft to 80 ft
    3. From 85 ft to 125 ft
    4. From 130 ft to 170 ft

 

  1. Factor:  49x2 – 36
    1. (7x – 6) (x + 6)
    2. (7x – 9) (7x + 4)
    3. (7x – 6) (7x + 6)
    4. (x – 12) (7x + 3)

 

  1. Mrs. Sego has saved $325 for a new refrigerator.  She plans to save an additional $50 per month.  What is the least number of months she will need to save money in order to have enough to buy a refrigerator that costs $760?
    1. 3 months
    2. 7 months
    3. 9 months
    4. 15 months

 

  1. The area of a rectangular floor is described by the equation:  w(w – 9) = 252  ;  where w is the width of the floor in meters.  What is the width of the floor?
    1. 12 m
    2. 14 m
    3. 16 m
    4. 21 m

 

  1. Factor:  15x2 – 5x3 – 10x2
    1. 5x2 (10x4 – x – 5)
    2. x2 (15x4 – 5x – 10)
    3. 5x3 (3x3 – x – 2)
    4. 5x2 (3x4 – x – 2)

 

  1. The area of a rectangle is given by the equation:  2w2 + w = 36  ;  where w is the width.  What is the width of the rectangle?
    1. 9
    2. 6
    3. 4.5
    4. 4

 

  1. Twenty-one less than a number is negative ninety-four.  What is the number?

 

78.  Rewrite the number:   0.000000052 , in scientific notation.

 

  1.  Rewrite the number:  0.000335 , in scientific notation.

 

  1. What number, when divided by six less than the number, is:  1 3/26?

 

  1. Solve the inequality:  g – 7/2 >13

 

82.  Solve the system by graphing:  Find the vertices of the graph.

                  X + 7y ≤ -14

                  X + y ≥ -2

                  2x – y ≤ 17

 

  1.  Solve the system by graphing:  Find the vertices of the graph.

X + y ≥ -9

6x + y ≤ -24

4x – y ≥ -16

 

  1. Solve the system by graphing:  Find the vertices of the graph.
    1. X + y ≤ -9
    2. 3x – 2y ≥ -2
    3. x – 4y ≤ 26

 

  1. The width of a rectangle is one-sixth the length.  The perimeter of the rectangle is one hundred sixty-eight feet.  What are the dimensions of the rectangle?

 

  1. The measure of two angles in a triangle are in the ratio of 4:5.  The third angle is 1080.    What are the measures of the two angles?

 

  1. Solve the system of equations using the substitution method.

14x + 3y = -226

 

-1/4y – 33/2 = x

 

  1. Solve the system of equations using the substitution method.

X = -91 – 3/2y

 

X + 3y = -145

 

  1. Simplify and write the answer in scientific notation.
    1. (6.8  x  105) (2 x 10-7)

4 x 106

 

  1. Solve each system of equations using any method.

4x + 19y = -502

x – 13y = 478

 

  1. Solve each system of equations using any method.

12x + 7y = 355

x – 8y = 124

 

  1. Mrs. Norrington wants to put a total of at least x stamps in 3 albums.  If she puts 44 stamps in the first album and 45 stamps in the second album, which inequality describes s, the number of stamps she should put in the third album?

A.  44 + 45 + x  ≥ x                 B.  s – (44 + 45) ≥ x                C.  (44)(45)(s) ≥ x

                        3

 

  1. Yesterday a total of 24 students were present in Mr. Rigel’s class.  There were 3 fewer girls than twice the number of boys.  Which system of equations can be used to find g, the number of girls who were present in Mr. Rigel’s class, and b, the number of boys who were present?

                  A.  g + b = 24              B.  g + b = 24              C.  g + b = 24             

                  g = 2b -3                      b = 2g - 3                     g = 2b + 3

 

  1. At which point does the graph of f(x) = x2 + 3x – 18 intersect the x-axis?
    1. (-9, 0) and (2, 0)
    2. (-6, 0) and (-3, 0)
    3. (-6, 0) and (3, 0)
    4. (-3, 0) and (6, 0)

 

  1. Which equation represents the line that passes through the point (-2, 8) and has a slope of -1/2?
    1. Y = -1/2x – 10
    2. Y = -1/2x – 9
    3. Y = -1/2x – 7
    4. Y = -1/2x + 7

 

  1. A truck is carrying 1500 pounds of cargo that occupies 138 cubic feet of space.  A television weighs 50 pounds and occupies a space of 4 cubic feet.  A microwave weighs 30 pounds and occupies a space of 3 cubic feet.  Which system can be used to find the total number of televisions, t, and microwaves, m, that are in the truck?
    1. 4t + 3m = 1500            b.  50t + 4m = 1500                 c.  50t + 30m = 1500

50t + 30m = 138               30t + 3m = 138                        4t + 3m = 138

 

  1. Simplify and write the answer in scientific notation.

6.3 x 10-5

5 x 107

 

  1. Simplify and write the answer in scientific notation

3 x 10-5

6 x 10-4

 

99.  Solve the inequality:   y – 2/3 ≥ 2/3

 

100.  Solve the inequality:  -3/4 ≤ n + ½

 

101.  Mrs. Cockerham, Mrs. Barrett, Ms. Lapp, and Mrs. Hickman raced to the auditorium.  Mrs. Cockerham beat Mrs. Hickman.  Mrs. Barrett finished before Mrs. Cockerham, but after Mrs. Mrs. Lapp.  Who won the race?

 

102.  Solve:  2 (n – 3) = -14         n = _____

 

103.  Mrs. Zacharias spent $1.24 for toothpaste.  She had quarters, dimes, nickels, and pennies.  How many dimes did she use if she used a total of 14 coins?

 

104.  Solve:   5 + 3 (b + 7) = 20       b = _____

 

105.  Mrs. Taulman set a goal to increase her running speed by 1 minute per mile every 5 weeks.  She starts out running 1 mile in 11 minutes.  If she can accomplish her goal, how many weeks will it take her to run a mile in 8 minutes?

 

106.  Solve:  8 (b – 1) = 5 (b + 4) + 8      b = _____

 

107.  A veterinarian’s office has a scale in the lobby to weigh pets.  The scale will weigh up to 250 pounds.  The following dogs are in the lobby:

 

Pepper       -23 pounds

Jack           -75 pounds

Trooper      -45 pounds

Precious     -25 pounds

Coco          -120 pounds

Which dogs could you put on the scale to get as close to 250 pounds as possible, without going over?  How much would they weigh?

 

108.  On her first check from Marko’s, 15% is withheld from Mary’s total earnings of $250.  What amount is withheld?

 

109.  Solve the equation x – y = 11, for y

A.     Y = x + 11

B.     Y = x – 11

C.     Y = -x + 11

D.     Y = -x - 11

 

 

 

110.  In the U.S. Congress, the number of representatives is 65 less than five times the number of senators.  There are a total of 535 members of Congress.  Find the number of senators and the number of representatives.

 

111.  A rectangular park has a perimeter of 1320 yd.  The length of the park is five times the width.  Find the length and width of the park.

 

112.Which line contains the point (-2, 4)?

A.     x – y = -2

B.     x + y = -2

C.     x – y = 2

D.     x + y = 2

 

113.  Of the total candy bars contained in the vending machine, 250 bars have been sold.  If 25% of  the bars have been sold, find the total number of candy bars that were in the machine.

 

114.  The recommended daily intake of iron for an adult female is 3 mg more than twice the recommended amount for a newborn infant.  The amount for an adult female is 15 mg.  How much should the infant receive?

 

115.What is the slope of the line that contains the points (-4,1) and (3, -7)?

  1. – 7/8
  2. -  8/7
  3. – 6/7
  4. – 8

 

 

116.  There are 680 computer chips in a secured storage area designed to hold 2000 computer chips.  What percentage of the storage area is filled?

 

117.  A cheetah’s sprinting speed is 25 miles per hour (mph) faster than a zebra can run.  The sum of their running speeds is 111 mph.  How fast can each animal run?

 

118.  What is the slope of the line y = -3x + 2?

  1. 3
  2. 2
  3. -3/2
  4. -3

 

119.  A board is 118 cm long.  Mrs. Rathert cut it into two pieces, with one piece 4 cm longer than the other.  Find the length of both pieces.

 

120.  Write the equation 5x – 2y = 10, in slope-intercept form.

 

 

 

121.  There have been 36 cups of coffee served from a banquet-sized coffee pot.  If this is 30% of the capacity of the pot, find the capacity of the pot.

 

122.  A medical clinic found that 16.8% of the patients were late for their appointments.  The number of patients who were late was 504.  Find the total number of patients.

 

123.  The perimeter of a rectangular building is 420 ft.  The length is four times as long as the width.  Find the length and the width.

 

124.  The sales tax on a new car is $820.  If the sales tax rate is 5%, find the price of the car before the sales tax is added.  What is the total cost including sales tax?

 

125.  State Troopers tested 924 school buses for safety.  There were 231 buses that failed the safety test for one or more reasons.  Find the percent of buses that failed the test.

 

126.  Joyce and her husband, Jim, spent a total of 19 hours redecorating their living room.  Jim spent 3 hours less than Joyce.  How long did each person work on the room?

 

127.  A $30,000 scholarship is being divided between two students so that one student receives three times as much as the other.  How much will each student receive?

 

128.  The sum of four times a number and 6 is -14.  Find the number.

 

129.  If a number is subtracted from five times the number, the result is 100.  Find the number.

 

130.  Sylvia bought two CD’s at $14.98 each.  The sales tax rate is 6%.  Find the total amount charged to Sylvia’s credit card.

 

131.  $1,000 in prize money is being split between Ron and Ryan.  Ryan should get $300 more than Ron.  How much will each man receive?

 

132.  Brian’s spachetti sauce recipe calls for 3 1/3 cups of tomato sauce.  He wants to make 2 ½ times the usual amount.  How much tomato sauce does he need?

 

133.  The Deaton family needs 35 ft of fencing to put around a rectangular garden plot.  If the plot is 6 ½ ft wide, find it’s length.

 

134.  Anita spent 25 minutes reading 14 pages in her sociology textbook.  At that rate, how long will it take her to read 30 pages? 

 

 

 

135.  A ball dropped from a height will bounce half the height of its previous bounce for the first two bounces.  When the ball hits the floor the third time, it will have traveled a total of 35 ft.  From what height was the ball dropped?

 

136.  A restaurant has 6 square tables, seating one person per side.  By doubling the number of tables, what is the least additional number of customers that can be seated?  Tables may be placed together to form larger tables, but they cannot be placed against the wall.

 

137.  The rectangular floor of a house is divided into two sections so that the length of the shorter section is x + 8 ft and the length of the longer is 45 ft.  The width of the rectangle is x ft.  What is an expression for the area of the floor?  What is the area of the floor if the value of x is 15?

 

138.  A school auditorium has 3 doors at the back and one on either side of the stage at the front.  It is possible to begin and end outside the auditorium by going through each door exactly once? 

 

139.  In basketball, there are 3-point shots, 2-point shots, and 1-point free throws.  If, as a part of scoring a total of 48 points, a team made 9 free throws, how many 3-point shots could they have made?

 

140.  The equation a2 – b2 = 16 can be satisfied by 6 different (a, b) ordered pairs.  One of the pairs is (5, 3), in which the difference a – b equals 2.  What is the greatest possible a – b difference?

 

141.  The sum of the first three odd numbers is 1 + 3 + 5 = 9.  What is the sum of the first 9 odd numbers?

 

142.  How does the sum of the first 9 even numbers compare to the sum of the first 9 odd numbers?  Explain why this is so.

 

143.  Two of the world’s tallest roller coasters Top Thrill Dragon (the taller of the two), in Ohio, and Steel Dragon, in Japan have a sum total height of 738 ft.  The difference in their heights is 102 ft.  What is the height of each roller coaster.

 

144.  There is a total of $3.35 in nickels and times on a table.  There are 13 more nickels than dimes.  How many nickels and how many dimes are there?

 

145.  A movie theater charges $8.50 for adults and $5.25 for children.  If four times as many adults as children paid for admissions and the total amount taken in was $902.75, how many  people paid in all?

 

146.  Practicing for a race, Lela increased the number of laps she ran on the track by 1 each day.  In all, she ran a total of 90 laps in less than 2 weeks.  On how many days could she have used the track?

 

147.  Mike took his monthly after-school job salary and spent $35 on CDs.  He put aside 25% of what remained for savings and 50% of what then remained towards a car.  He still has $60.  What was his salary?

 

148.  Ellie’s age is 75% of her sister Cheri’s.  Cheri is 3 years older than her brother Victor.  If Victor is 4 years older than his 13-year-old brother Robert, what is the age range of the siblings?

 

149.  At the end of a wedding party, 1/3 of the guests left first.  Then another 8 guests left.  There were still 32 people at the party.  How many guests attended in all?

 

150.  A book club will send you 6 books for $4.95 when you join.  After that, books cost $18.95 each.  What is the greatest number of books you can receive from the club if you spend less than $100?

 

151.  Some ballot measures require the approval of at least ¾ of those voting before a proposal can be come law.  What is the greatest number of voters that could have disapproved of a measure if there are 10,620 voters and measure passes?

 

152.  A DVD player is on sale for $29.99.  This reflects 30% off the original price.  What was the original price of the DVD player?

 

153.  Dolores bought 4 CDs, each at the same price, and paid with two $20 bills.  She received less than $5 as change.  What is the least each CD could have cost?

 

154.  The element sodium melts at 97.72oC.  It boils at 883oC.  What is the temperature range between the boiling point and melting point of sodium?

 

155.  The volume of a cylinder is approximately 2.65 m3.  It radius is 0.75 m.  Which is the best estimate of the cylinders height?

A.     15 m

B.     7.5 m

C.     2.0 m

D.     1.5 m

 

156.On four consecutive football plays, a team gains 7 yards, loses 3 yards, loses 4 yards, and gains 12 yards.  What is the average result of those four plays.  If the ball is 65 yards away from the end zone, how many plays will it take to score, given this average?

 

157.  In a NASA countdown, launch time is t = 0.  Time before a launch is negative and time after launch is positive.  What is the elapsed time from t minus 85 seconds to t plus 2 minutes 10 seconds?

 

158.  The faces of a number cube are numbered consecutively from 6 to 1.  Scoring is done by rolling the cube and multiplying your roll by your previous total.  In a game with 2 players, what is the greatest possible difference in scores after each player has taken 3 turns?

 

159.  The population of a particular bacterium in a lab experiment doubles every 15 minutes.  If the population at the start of an experiment is 2,000, what will it be after 3 hours?

 

160.  If you deposit $5,000 and leave it for 5 years at 6% interest, how much will you have?

 

161.  Betty deposited a multiple of $1,000 at an annual interest rate of 3%.  She forgot about it and left it in the bank for 30 years until she was ready to retire.  When she withdrew the money, she had $12,136.  How much did Betty originally deposit?

 

162.  A pizza with a 7-inch radius sells for $11.95, and one with an 8.5-inch radius sells for $14.99.  Which is the better buy, and by how much per square inch?

 

163.  Vienna Taxi charges according to the rule:  C = 0.45d where d is the number of ¼-mile segments.  The rule that Leota Taxi uses is C = 0.65m where m is th number of minutes.  For a 5-mile ride, averaging 20 mi/hr, which company would charge more?  How much more?

 

164.  The equation y = 5 (x – 3) describes the profit that a business earns from selling x T-shirts, where x is the number of shirts and y is the profit.  What is the company’s break-even point?

 

165.  A person who consumes 3,000 calories per day resolves to eat 100 fewer calories per day with every year he ages.  This relation can be described by a linear equation.  What would be the slope of the graph of the equation?

 

166.  The inequality describes the charges of a car rental agency: 

250 ≥ 159 + 39(d – 2)

The cost is $159 for the first 2 days and $39 per day after that.  If you can spend no more than $250, what is the greatest number of days you can keep a car?

 

167.A restaurant charges an average of $18.00 per dinner and has average expenses of $7.20 per meal served.  To stay in business, the owner must make a weekly profit of $2,000.  How many customers per week are needed to remain in business?

 

168.  On a map, the scale reads:  0.5 in = 25 mi.   How far apart are two cities that are 9.25 inches apart on the map?

 

169.  Bill has driven m2 – 3m + 9 miles west along a road from his home.  How many miles east must he drive to get back to his home if m = 5?

 

170.  The area of a volleyball court is 1,8000 ft2.  The equation x2 + 30x – 1,8000 = 0 can be used to find the dimensions of the court where x is the width.  What is the width of the volleyball court?

 

171.  A basketball and a golf ball were dropped from the same height.  The golf ball bounced twice as high as the basketball.  If the golf ball bounced to a height of 2h2 + 6 ft, how high did the basketball bounce?

 

172.  A company’s profit will follow the function:  P = -t2 – 4t + 96  The company will have zero profit in 2015.  If P represents profit and t is the number of years from when the information is given, in what year was the information given?

 

173.  A baseball pitcher is throwing a 93 miles per hour fastball.  How fast is the ball traveling in feet per second?

 

174.  If you drink 8 cups of water per day, how many gallons will you drink in one week?

 

175.  How many square yards are in one square mile?

 

176.  How many square inches are in one acre.

 

177.  Six students are running for 3 positions on the student council.  In how many ways is it possible for the 3 positions to be filled?

 

178.  A state’s license plates have 3 digits followed by 3 letters.  The digits cannot begin with 0.  Digits and letters can be repeated.   How many different license plates are possible?

 

179.  From 7 singers, how many ways can Mr. Childress choose 5 to sing solos at a holiday concert?

 

180.  From a bag with 8 marbles of which 2 are red, 2 are green, and 4 are white, Dennis picks one marble, does not replace it, and picks another.  What is the probability that Dennis picked 2 white marbles?