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# Introductory Math Word Problems Practice Quiz (page 2)

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1. c. The key phrase less than means "subtract from a number." Thus, three less than a number, n, is represented by the expression n – 3.
2. c. One strategy to use to solve this problem is to make an organized list. Since there are two choices of lunch, call one lunch A and the other lunch B. Because there are three choices of drinks, represent each as drink C, drink D, and drink E. Make a list of all possible choices containing exactly one lunch choice and one drink choice.
 Lunch A with drink C Lunch B with drink C Lunch A with drink D Lunch B with drink D Lunch A with drink E Lunch B with drink E

There are six different combinations in the list, so there are six possibilities.

1. b. Use the strategy of working backward to solve this problem. Begin with the \$7.00 he had left over at the end of the trip to the store. Then, do the opposite to work backward to find how much he had at the start. Add the \$2.00 he spent on a drink to get \$9.00, and add another \$1.00 for the ice cream cone to get \$10.00. At this point, he had spent half of his money on trading cards, so double \$10.00 to get the original amount of \$20.00.
2. d. Draw a Venn diagram to help with this question. The diagram should contain two circles that overlap, such as the following diagram. Label one circle band and the other chorus.

The 20 students in both band and chorus should be placed in the section where the two circles overlap. Since there are 60 total students in the band, this includes the 20 students in both groups. Therefore, there are 40 students in band only. In the same way, the 70 students in chorus represents the students in chorus only and in both groups, so there are 70 – 20 = 50 in chorus only. The completed diagram is shown next.

1. c. Use the strategy of solving a simpler problem by using smaller numbers of people in the office. If there were three people in the office, the first person would send three e-mails, the second would send two e-mails, and the third only one. Remember that there is only one e-mail between each pair of people. Thus, the pattern for three people is 3 + 2 + 1 = 6 e-mails. Therefore, the pattern for 14 people is 14 + 13 +12 + 11 + 10 + 9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1 = 105 e-mails.
2. b. The low temperature on Sunday was 14° below the low temperature on Saturday. To solve this problem, subtract: 9 – 14 = –5°.
3. b. To solve this problem, multiply cup of sugar by 3 for each dozen. cups of sugar.
4. c. Multiply 6 by the cost of an adult ticket: 6 \$7.50 = \$45.00. Multiply 5 by the cost of a student ticket: 5 × \$5.25 = \$26.25. Add these two amounts together to get the total spent on the tickets: \$45.00 + \$26.25 = \$71.25.
5. a. Divide the total miles by the total time traveled to find the rate.
6. miles per hour.

7. d. Set up the proportion:
8. Be sure to line up the units. Cross multiply to get 8x = 388.8. Divide each side of the equation by 8:

x = \$48.60

9. a. The key word of tells you to multiply 40% by 50. Change the percent to a decimal before multiplying: 0.40 × 50 = 20.
10. c. Find 4% of \$2,450 to find the total commission. Change the percent to a decimal before multiplying: 0.04 × \$2,450 = \$98.00.
11. a. Translate the statement from words into mathematical symbols. Let n = a number. Sum is a key word for addition and two times a number can be expressed as 2n. The equation is 5 + 2n = 27. Subtract 5 from each side of the equation to get 2n = 22. Divide each side of the equation by 2.
12. n = 11

13. c. Let n = the least number of buses needed. Since each bus can fit 51 students, the inequality is 51n ≤ 193. Divide each side of the inequality by 51:
14. n = 3.7843

This amount needs to be rounded, so there is enough room for all students.The least number of buses is 4.

15. d. To convert from scientific notation to standard notation, find the exponent on the base of 10. This exponent tells you how many places to move the decimal point; count to the right if the exponent is positive and to the left if it is negative. Start at the decimal point in 6.71 and count to the right eight places. Add zeros where necessary. The number becomes 671,000,000.
16. d. Let x = the number of pounds of the \$4.00 candy, and let 2x = the number of pounds of the \$2.00 candy. Write the equation:
\$2.00(2x) + \$4.00x = \$32.00
17. Multiply within the equation to get

4x + 4x = 32

Combine like terms to get

8x = 32

Divide each side of the equation by 8:

Thus

x = 4
2x = 2(4)
= 8

Janice bought 4 pounds of the \$4.00 candy and 8 pounds of the \$2.00 candy.

18. c. Let x = the smaller angle and let x + 10 = the larger angle. The term complementary means that the sum of the two angles is 90°. To write the equation, add the two angles and set the sum equal to 90:
x + x + 10 = 90
19. Combine like terms to get

2x + 10 = 90

Subtract 10 from each side of the equation: 2x + 10 – 10 = 90– 10 The equation simplifies to

2x = 80

Divide each side of the equation by 2:

x = 40

Therefore, the smaller angle is 40, and the larger angle is x + 10 = 40 +10 = 50°.

20. d. Let x = the measure of the first angle. Let x + 20 = the measure of the second angle. Let x + 40 = the measure of the third angle. The sum of the three angles of a triangle is equal to 180°, so add the three expressions and set the sum equal to 180:
x + x + 20 + x + 40 = 180
21. Combine like terms:

3x + 60 = 180

Subtract 60 from each side of the equation:

3x + 60 – 60 = 180 – 60
3x = 120

Divide each side of the equation by 3:

x = 40

Therefore, the first angle is 40°, the second angle is 40 + 20 = 60°, and the third angle is 40 + 40 = 80°. The largest angle is 80°.

22. b. Angle A and angle D in parallelogramABCD are consecutive angles, or angles that are next to each other. Therefore, the sum of their measures is 180°. If the measure of angle A is 85°, subtract 180 – 85 = 95 to find the measure of angle D. Angle D is 95°.
23. c. Use the given sides of both similar triangles to form a proportion. Let x = the longest side of the large triangle. Be sure to line up corresponding labels. The proportion could be set up as:

Substitute the given values:

Cross multiply to get 3x = 72. Divide each side of the equation by 3:

x = 24

The longest side of the larger triangle is 24 units.

24. b. Let x = the measure of the width, and let 2x + 5 = the measure of the length. Use the perimeter formula P = 2w + 2l. Substitute the let statements and the fact that the perimeter P = 70 to get the equation
70 = 2x + 2(2x + 5)
25. Use the distributive property to get:

70 = 2x + 4x + 10

Combine like terms:

70 = 6x + 10

Subtract 10 from each side of the equation:

70 – 10 = 6x + 10 – 10

The equation simplifies to:

60 = 6x

Divide each side of the equation by 6:

10 = x

Use the expression for the length (2x + 5) and substitute x = 10 to find the measure of the length:

2(10) + 5 = 20 + 5 = 25
26. d. The area of the circle can be found by using the formula A = π r2, where r is the radius of the circle. Because the question states that the answer is in terms of π, leave pi in your answer. The radius is 5, so substitute 5 into the formula: A = π(5)2 = 25π square units.
27. 23. c. First, find the area of the ceiling using the formula A = l × w. Since the length is 16 feet and the width is 10 feet, the area is 16 × 10 = 160 square feet. One can of paint is needed for every 75 square feet, so divide the total area by 75:
160 ÷ 75 = 2.133
28. Because this amount is more than 2, he will need to buy 3 cans of paint to cover the ceiling.

29. c. Find the surface area of the cylinder by using the formula SA = 2πr2, where r is the radius of the base, d is the diameter of the base, and h is the height of the cylinder. From the information in the problem, r = 2, d = 4 (double the radius), and h = 4. Substitute the given values into the formula and use π = 3.14159:
SA = 2(3.14159)(2)2 + (3.14159)(4)(4)
30. Evaluate the exponent:

SA = 2(3.14159)(4) + (3.14159)(4)(4)

Multiply in each term: SA = 25.13272 + 50.26544

Add to find the surface area:

SA = 75.39816

Round this value to the nearest tenth:

SA = 75.4 square inches
31. c. Use the formula volume = length × width × height (V = l × w × h). Substitute the given values into the formula:
V = 4 × 3 × 2.5
= 30 cubic inches
32. a. Use the slope formula:
33. Substitute the coordinates of the points. Use (2,4) for (x1,y1) and (–3,5) for (x2,y2). The formula becomes:

34. 27. c. The probability of an event E is equal to P(E) =
35. There are four even-numbered sections {2, 4, 6, 8}, so the number of ways the event can occur is 4. There are a total of 9 sections, so the total number of possible outcomes is 9. The probability is

36. d. The probability of an event E is equal to
37. There are 7 letters in the word ALGEBRA, so the total number of possible outcomes is 7. There is one G and three vowels in the word. Thus, the probability of selecting a G isand the probability of selecting a vowel is The probability of selecting a G or a vowel becomes

38. d. The total number of ways is equal to the number of permutations of five things taken five at a time. This is equal to 5 × 4 × 3 × 2 × 1 = 120 different orders.
39. b. The mode of a set of data is the value that occurs the most often. The value that appears the most in the list of data is 60 inches.

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