Download Lesson 8.6 Answers - Fort Thomas Independent Schools

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Name
Name
6-5B
8-5B
page 2
Questions on SPUR Objectives
See pages 549–551 for objectives.
SKILLS Objective B
37%
9. Carlos had a 10% off coupon and spent it on a computer game that was
marked down 30%. What was his total discount?
8-6A Lesson Master
In 1−3, solve mentally.
10. After a discount of 20%, the dress Sharon wanted was $85. What was
the original price of the dress?
$106.25
1. 6x = 18
2. 48 = 8m
3
x=
11. A collectible comic book worth $40 two years ago gained 15% in
value the next year, but then lost 15% in value this year. What is it
worth now?
$39.10
12. A piece of property increased in value by 14% in one year and by 10%
in the next year. What was the percent of increase over the two years?
4. 15q = 50
25.4%
14. The price of an item in a store is reduced by 50%. Then the price is
reduced by another 50%. What is the total percent change as a result
of the two discounts?
7.5
d=
In 4−6, use the Multiplication Property of Equality to solve the equation.
Check your answer.
5. 4.2 = 0.14r
q = 3 _3
2.6% increase
in value
13. A piece of property increased in value by 14% in one year and
decreased in value by 10% the next year. What was the percent
change in value over the two years?
3. 10d = 75
6
m=
1
6. 75% of s = 15
r = 30
PROPERTIES
s = 20
Objective E
7. What does the Multiplication Property of Equality allow you to do?
Why is this procedure useful?
75%
15. Explain why the cost of an item discounted 20% can be calculated by
multiplying the original price by 0.8.
Let P be the original price. Then 0.2P is the
discount amount and P - 0.2P is the cost.
Using the Distributive Property, P - 0.2P = 0.8P.
8.
It allows you to multiply both sides of an equation by
the same number. It can be used to solve equation
involving multiplication.
30y
Fill in the blank. If x = 3y, then 10x =
.
9. To solve 60 = 1.5m, what should be done to both sides of the equation?
1
Multiply sides by ___
1.5 .
USES Objective G
16. Explain why the cost of an item discounted 20% and then taxed 8%
can be calculated by multiplying the original price by 0.864.
Let P be the original price. Then 0.2P is the
discount amount and P - 0.2P = 0.8P is
the cost before taxes. The cost with 8% tax is
1.08(0.8P) = 0.864P
In 10−12, write an equation of the form ax = b for each situation, and then
solve the equation.
10. A rectangle has area 475 ft2 and width 25 ft. Find its length.
25 · L = 475
equation:
L = 19
answer:
11. At Liddle Middle School, 32% of the students are 7th graders. If there
are 112 students in the seventh grade, how many students are in the school?
0.32 · s = 112
equation:
s = 350
answer:
12. At a speed of 17 miles per second, approximately how many hours
would it take a spaceship to travel to the moon, a distance of 239,000 miles?
17 · t = 239,000; t ≈ 14,059
seconds; 60 · 60 · h = 14,059
equation:
Transition Mathematics
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Name
8-6B Lesson Master
SKILLS
8-6B
Objective B: Solve and check equations of the form ax = b
page 2
PROPERTIES
Objective E: Recognize and use the Multiplication Properties of
Equality and Inequality.
and ax + b = c.
21. Give an instance of the Multiplication Property of Equality.
In 1−9, give the reciprocal of each expression.
1. −5
− _15
4. −1.8
−5
__
2. − __49
−1
__
1
3. __6
− _94
6. −2 __34
5. 1
1
9
7. −e
1
8. __e
e
6
Tom multiplied both sides by ; Tim multiplied both sides
by 4; They both got x = −8 as the answer.
−4
__
11
−m
9. ___
n
e
n
__
23. Multiple choice. What should be done to the equation __45 y = 20 to
solve for y?
−m
10. 3x = 42
11. 4t = −34
12. −d = 40.9
13. −9y = 54
14. −104 = −4r
−8
15. ___
5 x = 96
16. −7.4k = 111
17. −9 = −25g
x = 14
d = −40.9
r = 26
k = −15
5
−1
__
18. ___
8 q = 24
−5
_2
q = __
3 or −1 3
20. 4d + 2d = −16
d = −2 _23
t = −8.5
y = −6
x = −60
9
g = __
25 or 0.36
−4
B Multiply both sides by ___
.
5
C Divide both sides by __54 .
−4
D Divide both sides by ___
.
5
USES
Objective G: Find unknowns in real situations involving
multiplication.
In 24−27, write an equation of the form ax = b for each situation, and then
solve the equation.
24. Mrs. Doherty wants to make a 150-square foot rectangular vegetable
garden along the side of her garage. If the garage is 20 feet long, how
wide should the garden be?
answer
25. Four-fifths of a number is 212. What is the number?
_4 n = 212
5
n = 265
equation
REVIEW
answer
Chapter 2, Objective C
In 26−31, translate into a mathematical expression.
12 - 8
8 < 12
_1
6 more than half a number 2 n + 6
8 - 12
(11)(17)
6 decreased by twice a number 6 - 2n
26. twelve less 8
27. twelve less than 8
28. Eight is less than 12.
29. the product of 11 and 17
30.
31.
Transition Mathematics
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x = 7.5 ft
20x = 150
equation
x = −0.1425
t = 0.2
A
A Multiply both sides by __54 .
19. 3.2x = −0.456
1
21. __2 t - 4t = −0.7
Sample: If 2p = 5,
then 10p = 25.
22. Given the equation __34 x = −6, Tom wrote __14 x = −2, and Tim wrote
3x = −24. Show why both Tim and Tom are correct, and solve the equation.
_1
3
In 10−19, solve and check.
A52
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395
Copyright © Wright Group/McGraw-Hill
Name
394
h ≈ 3.9
answer:
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