Concept Review 5
1.x, y,or any unknown; ×; is;÷ 100
2.
- 1.30 4. 0.81 5. 2.20 6. − 20
7.
- .35x= 28 x= 80
- 60 =.15xx= 400
- 175%. Rephrase: What percent of 20 is 35?(or re-
member is over ofequals the percent)
3,500 = 20 xx=175(%)
- 25%. Use the “percent change” formula:
1 500 1 200
1 200
100
300
1 200
100 25
,,
,
%
,
%%
−
×= ×=
xx
100
20 35
35
20 100
×= or =
5
100
=× = 26 19 23
x
x .%
final amount starting amount
starting amount
−
××100%
12.
13. 40%.
- To increase a number by 30%, multiply by
1.30: 20 ×1.30 =26.
- To increase a number by 30%, multiply by
- 0.96. x(1.20)(.80) =0.96x
- Because the two percentages are “of” different
numbers. - 9.75%. Assume the original square has sides of
length xand area x^2. The new square, then, has
sides of .95xand area of .9025x^2. - 50% of 28, which equals 14
- 25% of 48, which equals 12
.
%
.
%.%
9025
100
0975
100 9 75
22
2
2
2
xx
x
x
x
−
×=
−
×=−
44 800 32 000
32 000
100
12 800
32 000
100
,,
,
%
,
,
%
−
×= ×= 4 40%
−
−
×=
−
15 ×=−
168 80
80
100
12
80
%. % 100 % 15 %
Answer Key 5: Percents
290 MCGRAW-HILL’S SAT
SAT Practice 5
- D Miscellaneous expenses =$3,500 −$2,200 −$600
=$700. As a percent of the total, 700/3,500=20%. The
total number of degrees in a pie graph is 360°, so the
sector angle =20% of 360°=.20 × 360 = 72 °. - 32% Assume the starting price is x.The final
price is x(1.20)(1.25)(.80)(1.10) = 1.32x,which
represents a 32% increase. Notice that you can’t
just “add up” the percent changes, as we saw in
Question 16 of the Concept Review. - C The total number of points is 40 + 80 =120.
The number of points she earned is .60(40) +.90(80)
= 24 + 72 =96. 96/120 =.80 =80%. - D If you chose (A), remember: 2/3% is NOT the
same thing as 2/3! Don’t forget that % means ÷100.
x=2/3% of 90 =(2/3) ÷ 100 × 90 =0.6
1 −0.6 =0.4 - C If you chose (B), remember that the tax is 5%
of the starting amount, not the final amount. The
final price must be 5% higher than the starting
price. If the starting price is x,then $8.40 =1.05x.
Dividing by 1.05, x=$8.00.
6. B Let a=population of Town A, b=population
of Town B, and c=population of Town C. Since b
is 50% greater than a, b=1.50a.Since cis 20%
greater than a, c=1.20a.
You can also set a=100, so b=150 and c=120.
- C If the rectangle has length aand width b,then
its area is ab.The “new” rectangle, then, has
length 1.2aand width 1.3band so has an area of
1.56ab,which represents an increase of 56%. - C The total amount of salt is .30(12) +.60(24)
=3.6 +14.4 =18 ounces. The total amount of so-
lution is 36 ounces, and 18/36 =50%. Or you might
notice that 24 is twice as much as 12, so the con-
centration of the mixture is the average of “two
60s and one 30.”
(60% +60% +30%)/3 =50% - D The number of girls is n+45, so the total num-
ber of students is 2n+45. So the percentage of
girls is
100 45
245
n
n
()+
+
%
15 12
12
100
3
12
100 25
..
.
%
.
.
%%
aa
a
a
a