Math 87 Enrichment Answers and Notes

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1i) a.

1g) Answers will vary depending on the size of the group: $9.80 x number of students in the group.

1f) Answers will vary.

2i) a.

2g) Answers will vary.

2f) Answers will vary.

3i) b.

3g) Answers will vary. Divide the total by the number of students in the group to find the average.

3f) Answers will vary; 2/4 and 1/2 are possible equivalent fractions for 4/8.

4i) c.

4g) Answers will vary.

4f) 2 pizzas = 16 slices

16/16 - 2/16 - 2/16 - 2/16 = 10/16 of the slices remain after 3 people have taken 2 slices each.

10/16 - 1/16 - 1/16 - 1/16 = 7/16 of the slices remain after 3 more people have taken 1 slice each.

5i) a.

5g) c.

5f) d. 50 weeks in 350 days: 50 x 40 = 2000; 52 weeks in a year: 2 x 40 = 80, 2000 + 80 = 2080

6i) d.

6g) a.

6f) $42.18/6 can be simplified to $42.00/6 = $7.00 and $0.18/6 = $0.03. Therefore, $42.18/6 = $7.03. A twelve-month subscription would cost $7.03 x 12 = $84.36.

7i) c.

7g) Answers will vary; five possible values are b= 6 and h = 8, b= 12 and h = 4, b= 2 and h= 24, b= 8 and h= 6, and b= 4 and h= 12.

7f) Answers will vary.

8i) b.

8g) Answers will vary.

8f) Answers will vary. Express the answer as page number/number of pages in the book.

9i) a.

9g) 1000 x 1000 = 103 x 103 = 106; 1,000,000 x 1,000,000 = 106 x 106= 1012; 1,000,000,000 x 1,000,000,000 = 109 x 109 = 1018

9f) See textbook for examples of numbers written in scientific notation.

10i) c.

10g) Answers will vary.

10f) Answers will vary. If you add 10 years to everyone's age, the average will be 10 years higher.

11i)

  1. a.
  2. c.
  3. a.

11g) Both arithmetic problems have the same answer, -3, which shows that the operation of subtracting a negative number is the same as adding a positive number.

11f)

  1. +4
  2. -9

12i) d.

12g) Answers will vary.

12f) If your child's calculated answer was different from the time it took him or her to walk the distance, some reasons may be that the length of the blocks differed, the child's walking speed decreased or increased, or other conditions were different.

13i)

  1. b.
  2. a.
  3. c.

13g) Answers will vary.

13f) Answers will vary.

14i)

  1. c.
  2. a.
  3. c.

14g) Answers will vary.

14f)

  1. 5.355 x 1010
  2. 4.644 x 103
  3. 5.166 x 10-12

15i)

  1. c.
  2. a.
  3. b.

15g)

  1. One possible answer is (3am4) (3am4).
  2. One possible answer is (2x2) (1.6a-2).
  3. (25z-18g-3) (4z12g-6)

15f)

  1. 0.651x4 yz2
  2. -168g2h5k5
  3. -46.62abc

16i)

  1. b.
  2. c.
  3. a.

16g) The magazines cost 2m dollars. If you have n students in your group, you have n dollars to spend. n = 2m or m= n/2 dollars can be spent per magazine.

16f)

  1. 6a= -12, so a = -2
  2. 5/2a= 5/3, so a = 2/3
  3. 7/2b= 12/4 + 3/4 = 15/4, so b= 30/28 = 15/14

17i) b.

17g) The distance to the first rest stop is 3 miles. The distances of the second and third parts of the hike are 41/2 miles and 2 miles respectively.

17f) Answers will vary.

18i)

  1. a.
  2. c.
  3. b.

18g)

  1. c.
  2. a.
  3. b.

18f)

  1. 37 degrees Celsius
  2. 0 degrees Celsius
  3. Answers will vary.

19i) x2 = 402 + 302 = 2500; x = 50 ft to walk diagonally across the yard; 30 + 40 = 70 ft to walk around two sides of the yard; 70 - 50 = 20 ft shorter to walk diagonally across the yard

19g) Another Pythagorean triplet is 5, 12, and 13.

19f) x2 = 122 + 82 = 208 ft2; x = 14.4 ft; x2 = 102 + 82 = 164 ft2; x = 12.8 ft

20i) b.

20g) 30 gallons times 3.8 liters per gallon = 114 liters of water; 114 liters of water = 114 kilograms of water; 114 kilograms of water + 4.5 kilograms when empty = 118.5 kilograms total

20f) Answers will vary.