R14 Selected Answers and SolutionsSelected Answers and Solutions
If the kids follow the path to the cabin, to the mess
hall, and fi nally to the campfi re, they will walk
17 units. We are given the key that 1 square = 75 yards.
Write a proportion to fi nd the total distance walked.
units →
yards →^_^1
75 =(^17)
x^
← units
← yards
1 · x = 17 · 75 Find cross products.
x = 1,275 Simplify.
The kids walk 1,275 yards from the time they leave
the lake until they get to the campfire.
By the time they return to the cabin for bed, they
will have walked a total of 30 units.
units →
yards →^
^1
75 =
^30
x^
← units
← yards
1 · x = 30 · 75 Find cross products.
x = 2,250 Simplify.
The kids walk 2,250 yards total from the time they
leave the lake until they go to bed.
13a. true; Sample answer: All squares have 4
90° angles and equal sides. Therefore, all squares
are proportional to other squares. 13b. false;
Sample answer: Rectangles have different
lengths than widths that may not be proportional
to another rectangle. 15. 20 cm 17. Sample
answer: The corresponding sides have ratios of
^3
4.5^ ,
^5
7.5^ , and
2.8
4.2^. All three ratios simplify to
^2
3. Since
corresponding sides are proportional, the triangles
are similar. 19. 4; 12 21. Sample answer: When
two triangles have an equal corresponding angles
formed by proportional corresponding sides, the
triangles are similar.
Pages 301–302 Lesson 5-3B
11 x^ =^38 (^
^18
12 )^ Multiply by the scale factor.
19
x= ^381 ( ^1812 ) Cancel common factors.
6
x= 57 Simplify.
The perimeter is 57 millimeters.
- 78.75 in^2 5. 14.55 in. 7. 49 ft^2
99 x^ = 1,134 (^ _ 31 )^
2
Multiply the square of the scale factor.x= 1,134 ( 19 _ (^) ) Evaluate the power.
x= 126 Multiply.
The area of the putting green will be 126 square feet.
- Sample answer:
10 m
5 m
12 m6 m
P = 30 m P = 36 m
A = 50 m^2 A = 72 m^2- Robert is thinking of size in terms of area and
Denise is thinking of size in terms of perimeter. - H 17. 27 yd 19. 1 in. = 60 mi
Pages 306–309 Chapter Study Guide and Review - proportional 3. proportion 5. unit rate 7. scale
9. nonproportional 11. 90 mi per day 13. No; the
ratios are not equal. 15. 4 17. 3.5 19. 12.5
21. 3.2 mi 23. 25 minutes 25. 21 km 27. 1 in. =
24 in. or 1 in. = 2 ft 29. RUTS 31. 4.2 ft 33. 150 yd^2
Chapter 6 Percent
Page 316 Chapter 6 Are You Ready?
48 3. 1,512 5. $54.75 7. 0.17 9. 1.57 11. 0.085
0.075 15. 8% 17. 580% 19. 72.5%
Pages 322–324 Lesson 6-1B
4 3. 110.5 5. 23 7. $3.25 9. $194.40 11. 45.9
14.7
1515 Method 1 Write the percent as a fraction.
175% = ^175100 or^7 4
7 4 of 10 = 47 × 10
= ^74 × ^101 or 17 21
Method 2 Write the percent as a decimal.
175% = ^175100 or 1.75
1.75 of 10 = 1.75 × 10 = 17.5
62.5 19. $290 21. 3.5 23. 97.8 25. 92.5
about 19.5 million 29. 3.3 31. 990 33. 520
0.24 37. $241.50 39. $297 41. about 30
about 15
4545 There are 20 answers on the test. If 25% of the
answers are choice B, there are 0.25 × 20 or
5 answers that are choice B. Subtracting these 5
from the total number of 20 answers leaves
15 answers that are not choice B.
47a. 66.7% 47b. 33.3% 47c. 50% 47d. 33.3%
C 53. I 55. 124
Pages 327–330 Lesson 6-1C
5;^1 2 · 10 = 5; 0.1 · 10 = 1 and 5 · 1 = 5
33 Method 1: Use a fraction to estimate.
38% is about 40% or ^25.
38% of 62 ≈ 2 _ 5 · 60 or 24
Method 2: Use 10% to estimate.
10% of 60 is 6.
38% is about 4 · 10%.
4 · 6 = 24
So, 38% of 62 is about 24.
105; (1 · 70) + ( 21 · (^70) ) = 105 7. about 48
teenagers; ^35 · 80 = 48; 0.1 · 80 = 8 and 8 × 6 = 48
35;^1 _ 2 · 70 = 35; 0.1 · 70 = 7 and 5 · 7 = 35
1111 Estimate 21% of 90.
Method 1 Use a fraction to estimate.
21% is about 20%, or _^15.
20% of 90 = _^15 × 90 or 18.R01_R42_EM_SelAns_895130.indd R14 1/18/10 9:51 AM