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Math Problems
Grade 8
Find what percent one number is of another: word problems
After a month of successful fundraising, Jeffrey and his classmates voted on whether to donate the money they had raised to hunger relief or to environmental causes. Out of
40
40
40
votes,
16
16
16
were for hunger relief. What percentage of the votes were for hunger relief
\newline
Write your answer using a percent sign (
%
\%
%
).
\newline
_____
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At the craft store, Darell bought a bag of red and orange marbles. He received
100
100
100
marbles in all.
60
60
60
of the marbles were red. What percentage of the marbles were red?
\newline
Write your answer using a percent sign (
%
\%
%
).
\newline
_
_
_
\_\_\_
___
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The students in Carly's class got to choose between pizza and burgers for the celebration on the last day of school.
10
10
10
students picked the pizza. If there are
40
40
40
students in all in Carly's class, what percentage of the students picked the pizza?
\newline
Write your answer using a percent sign (
%
\%
%
).
\newline
_____
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Emilio's Burgers cooks its burgers either well done or medium. Last night the restaurant served
70
70
70
burgers in all,
14
14
14
of which were well done. What percentage of the burgers were well done?
\newline
Write your answer using a percent sign (
%
\%
%
).
\newline
_
_
_
_
_
\_\_\_\_\_
_____
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Ian's Diner offers its clients a choice of regular and diet soda. Last night, the diner served
90
90
90
sodas in all,
9
9
9
of which were regular. What percentage of the sodas were regular?
\newline
Write your answer using a percent sign (
%
\%
%
).
\newline
_____
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10
10
10
out of the
50
50
50
employees at the water slides are temporary employees. What percentage of the employees at the water slides are temporary?
\newline
Write your answer using a percent sign (
%
\%
%
).
\newline
_____
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Oliver's Cafe offers two kinds of espresso: single-shot and double-shot. Yesterday afternoon, the cafe sold
72
72
72
espressos in all,
54
54
54
of which were single-shot. What percentage of the espressos were single-shot?
\newline
Write your answer using a percent sign (
%
\%
%
).
\newline
_____
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show, how much amount has been collected?
\newline
9
9
9
. Nine boards are stacked on the top of each other. The thickness of each board is
3
2
3
c
m
3 \frac{2}{3} \mathrm{~cm}
3
3
2
cm
. How high is the stack?
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Wesley's Cafe offers two kinds of espresso: single-shot and double-shot. Yesterday afternoon, the cafe sold
50
50
50
espressos in all,
25
25
25
of which were single-shot. What percentage of the espressos were single-shot?
\newline
Write your answer using a percent sign (%).
\newline
_
_
\_\_
__
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At Wendy's Beading Boutique,
20
20
20
out of the
40
40
40
beads on clearance are plastic. What percentage of beads on clearance are plastic?
\newline
Write your answer using a percent sign (
%
\%
%
).
\newline
_____
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24
24
24
out of the
30
30
30
students at a school assembly were first-grade students. What percentage of the students at the assembly were first-graders?
\newline
Write your answer using a percent sign (%).
\newline
_____
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Evan's town voted on a new speed limit. Out of
70
70
70
votes,
7
7
7
were in favor of the new speed limit. What percentage of the votes were in favor of the new speed limit?
\newline
Write your answer using a percent sign (%).
\newline
_____
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At Gina's Hats,
81
81
81
out of the
90
90
90
hats at the store are baseball caps. What percentage of hats at the store are baseball caps?
\newline
Write your answer using a percent sign (%).
\newline
_____
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For a company picnic, Maddie ordered a box of fresh-baked gingerbread cookies and sugar cookies. She got
60
60
60
cookies in all.
12
12
12
of the cookies were gingerbread. What percentage of the cookies were gingerbread?
\newline
Write your answer using a percent sign (%).
\newline
_
_
_
_
\_\_\_\_
____
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This morning, Tanvi took a history test. She got
16
16
16
out of
40
40
40
problems right. What percentage did Tanvi get right?
\newline
Write your answer using a percent sign (%).
\newline
_____
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The city council voted on a new tax.
45
45
45
council members voted in favor of the tax. The council has
50
50
50
members. What percentage of the council members voted in favor of the tax?
\newline
Write your answer using a percent sign (%).
\newline
_____
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Edgar's Burgers cooks its burgers either well done or medium. Last night the restaurant served
40
40
40
burgers in all,
4
4
4
of which were well done. What percentage of the burgers were well done?
\newline
Write your answer using a percent sign (%).
\newline
_____
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There are
50
50
50
students in Percy's grade.
25
25
25
of the students are enrolled in health. What percentage of the students are enrolled in health?
\newline
Write your answer using a percent sign (%).
\newline
_____
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At Elena's Beading Boutique,
15
15
15
out of the
30
30
30
beads on clearance are plastic. What percentage of beads on clearance are plastic?
\newline
Write your answer using a percent sign (
%
\%
%
).
\newline
_____
Get tutor help
81
81
81
out of the
90
90
90
magazines at the bookstore are women's magazines. What percentage of the magazines at the bookstore are women's magazines?
\newline
Write your answer using a percent sign (%).
\newline
_
_
_
_
_
%
\_\_\_\_\_\%
_____%
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Paula's Tea Shop has caffeinated tea and decaffeinated tea. The tea shop served
40
40
40
teas in all,
28
28
28
of which were caffeinated. What percentage of the teas were caffeinated?
\newline
Write your answer using a percent sign (%).
\newline
_____
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The city council voted on a new tax.
30
30
30
council members voted in favor of the tax. The council has
50
50
50
members. What percentage of the council members voted in favor of the tax?
\newline
Write your answer using a percent sign (%).
\newline
_____
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The cafeteria director at Great Minds School wants to know what percent of the students would choose vegetarian entrees if they were available.
\newline
Which of the following survey methods will allow the director to make a valid conclusion about the percentage of students who would choose vegetarian entrees?
\newline
Choose
1
1
1
answer:
\newline
(A) Sort a list of the students into a random order, then ask the first
35
35
35
students on the list.
\newline
(B) Ask the first
35
35
35
students in line for the cafeteria.
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80
,
80
,
60
,
95
,
70
80,80,60,95,70
80
,
80
,
60
,
95
,
70
\newline
What is the mean of the values shown?
\newline
Choose
1
1
1
answer:
\newline
(A)
60
60
60
\newline
(B)
76
76
76
\newline
(C)
77
77
77
\newline
(D)
80
80
80
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John and Mary have some marbles. The total number of marbles with John and Mary is
75
75
75
times the ratio of the number of marbles with John to that with Mary. If Mary has
30
30
30
marbles, find the number of marbles with John.
\newline
(A)
20
20
20
\newline
(B)
30
30
30
\newline
(C)
45
45
45
\newline
(D)
50
50
50
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The amount of medication in Rory's bloodstream decreases at a rate that is proportional at any time to the amount of the medication in the bloodstream at that time.
\newline
Rory takes
150
150
150
milligrams of medication initially. The amount of medication is halved every
13
13
13
hours.
\newline
How many milligrams of the medication are in Rory's bloodstream after
8
8
8
hours?
\newline
Choose
1
1
1
answer:
\newline
(A)
98
98
98
\newline
(B)
104
\mathbf{1 0 4}
104
\newline
(C)
204
204
204
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The student population at University X consists of
63
%
63 \%
63%
undergraduate students and
37
%
37 \%
37%
graduate students. If
23
%
23 \%
23%
of undergraduate students and
42
%
42 \%
42%
of graduate students wear contacts, what percent of all students wear contacts?
\newline
Choose
1
1
1
answer:
\newline
(A)
14.5
%
14.5 \%
14.5%
\newline
(B)
15.5
%
\mathbf{1 5 . 5 \%}
15.5%
\newline
(C)
30.0
%
30.0 \%
30.0%
\newline
(D)
75.0
%
\mathbf{7 5 . 0 \%}
75.0%
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An organization determined most of its sales only occurred after at least
4
4
4
contacts. However,
44
%
44 \%
44%
of its salespeople gave up on a customer after the
1
st
1^{\text {st }}
1
st
contact didn't make a sale. Of the remaining salespeople,
40
%
40 \%
40%
gave up after the
2
nd
2^{\text {nd }}
2
nd
contact. Finally,
41
%
41 \%
41%
of the salespeople who made a
3
rd
3^{\text {rd }}
3
rd
contact gave up when that call did not make a sale. To the nearest percent, what percent of the original salespeople made
4
4
4
or more contacts if the first
3
3
3
contacts did not result in sales?
\newline
(Round to the nearest percent. Ignore the
%
\%
%
symbol when entering your answer. For example, if the answer is
11.2
%
11.2 \%
11.2%
, enter
11
11
11
.)
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Fabrizzio went shopping on Tuesday and decided to purchase a pair of pants that is
15
%
15 \%
15%
off the regular price. If he waits and buys the pants on Wednesday, he will receive an additional
5
%
5 \%
5%
off. What percent would Wednesday's sale price be of the original price for the pants? Round to the nearest whole percent.
\newline
Choose
1
1
1
answer:
\newline
(A)
81
%
81 \%
81%
\newline
(B)
85
%
85 \%
85%
\newline
(C)
95
%
95 \%
95%
\newline
(D)
105
%
105 \%
105%
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Owen answered a set of math and history Quiz Bowl questions. Owen correctly answered
72
%
72 \%
72%
of all the
200
200
200
questions. However, Owen answered
53.3
%
53.3 \%
53.3%
of the math questions correctly. If
45
%
45 \%
45%
of the questions were in math, what percent of history questions did Owen answer correctly?
\newline
(Round to the nearest percent. Ignore the
%
\%
%
symbol when entering your answer. For example, if the answer is
11.2
%
11.2 \%
11.2%
, enter
11
11
11
.)
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The chef has
36
36
36
pounds of strip loin steak. The amount of weight lost from the trim on each pound is
35
%
35 \%
35%
, and
75
%
75 \%
75%
more of the steak's weight is lost after cooking it. How many pounds of trimmed, cooked strip loin will the chef have left to serve to the customers?
\newline
Choose
1
1
1
answer:
\newline
(A)
5
5
5
.
85
85
85
\newline
(B)
12.6
12.6
12.6
\newline
(C)
17.55
17.55
17.55
\newline
(D)
23
23
23
.
4
4
4
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Which of the following percent values is equivalent to
42
42
42
out of
50
50
50
?
\newline
Choose
1
1
1
answer:
\newline
(A)
42
%
42 \%
42%
\newline
(B)
80
%
80 \%
80%
\newline
(C)
84
%
84 \%
84%
\newline
(D)
92
%
92 \%
92%
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Of the
50
50
50
U.S. states,
4
4
4
have names that start with the letter W. What percent of U.S. states have names that start with the letter W?
\newline
(Ignore the
%
\%
%
symbol when entering your answer. For example, if the answer is
12
%
12 \%
12%
, enter
12
12
12
.)
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If
5
5
5
is
d
%
d \%
d
%
of
8
8
8
, what is the value of
d
d
d
? (Ignore the
%
\%
%
symbol when entering your answer. For example, if the answer is
12.4
%
12.4 \%
12.4%
, enter
12
12
12
.
4
4
4
.)
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Avocado farmers use the percent of dry matter, the matter left after dehydration, from sample avocados in their orchards to determine the best time to harvest the avocados. If a sample of the flesh of the avocado weighs
10
10
10
grams (g) before dehydration, and
1.8
g
1.8 \mathrm{~g}
1.8
g
after dehydration, what was the percent of dry matter in the sample? (Ignore the
%
\%
%
sign when entering your answer. For example, if the answer is
12
%
12 \%
12%
, enter
12
12
12
.)
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Esteban has a big jar of change in his room. He has
600
600
600
coins total, and
240
240
240
of them are pennies. What percent of the coins are pennies?
\newline
(Ignore the
%
\%
%
symbol when entering your answer. For example, if the answer is
11
%
11 \%
11%
, enter
11
11
11
.
)
)
)
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A coin contains
1
1
1
.
25
25
25
grams of nickel and
3
3
3
.
75
75
75
grams of copper, for a total weight of
5
5
5
grams. What percent of the metal in the coin is copper?
\newline
(Ignore the
%
\%
%
symbol when entering your answer. For example, if the answer is
11
%
11 \%
11%
, enter
11
11
11
.)
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There are
25
25
25
students in Ms. Nguyen's second-grade class. In the class election,
4
4
4
students voted for Benjamin,
12
12
12
voted for Sahil, and
9
9
9
voted for Maria. What percent of the class voted for Maria?
\newline
(Ignore the \% symbol when entering your answer. For example, if the answer is
11
%
11 \%
11%
, enter
11
11
11
.
)
)
)
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In our solar system,
6
6
6
of the
8
8
8
planets have moons. What percent of the planets have moons?
\newline
(Ignore the
%
\%
%
symbol when entering your answer. For example, if the answer is
11
%
11 \%
11%
, enter
11
11
11
.)
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In the United States,
13
13
13
out of every
20
20
20
cans are recycled. What percent of cans are recycled?
\newline
(Ignore the
%
\%
%
symbol when entering your answer. For example, if the answer is
11
%
11 \%
11%
, enter
11
11
11
.)
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Of all the species in the world,
4
4
4
out of every
5
5
5
are insects. What percent of species are insects?
\newline
(Ignore the
%
\%
%
symbol when entering your answer. For example, if the answer is
11
%
11 \%
11%
, enter
11
11
11
.)
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A gumball machine contains
23
23
23
green gumballs,
52
52
52
red gumballs,
34
34
34
blue gumballs,
61
61
61
yellow gumballs, and
30
30
30
pink gumballs. What percent of the gumballs are red?
\newline
(Ignore the
%
\%
%
symbol when entering your answer. For example, if the answer is
12
%
12 \%
12%
, enter
12
12
12
.)
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Layla and Nathan each sent out college recruitment e-mails to different prospective students. Students followed a link to get more information from
22
%
22 \%
22%
of Layla's
400
400
400
e-mails and from
60
60
60
out of
350
350
350
of Nathan's e-mails. To the nearest percent, what percent of the total students clicked on the link from the e-mails?
\newline
(Ignore the
%
\%
%
symbol when entering your answer. For example, if the answer is
12
%
12 \%
12%
, enter
12
12
12
.)
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The earth has a mass of approximately
6
⋅
1
0
24
6 \cdot 10^{24}
6
⋅
1
0
24
kilograms
(
k
g
)
(\mathrm{kg})
(
kg
)
. The volume of the earth's oceans is approximately
1.34
⋅
1
0
9
1.34 \cdot 10^{9}
1.34
⋅
1
0
9
cubic kilometers
(
k
m
3
)
\left(\mathrm{km}^{3}\right)
(
km
3
)
, and ocean water has a mass of about
1.03
⋅
1
0
12
k
g
k
m
3
1.03 \cdot 10^{12} \frac{\mathrm{kg}}{\mathrm{km}^{3}}
1.03
⋅
1
0
12
km
3
kg
. To the nearest hundredth of a percent, what percent of the earth's mass is from the oceans?
\newline
(Ignore the
%
\%
%
symbol when entering your answer. For example, if the answer is
0.11
%
0.11 \%
0.11%
, enter
0
0
0
.
11
11
11
.)
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In a community service class in the fall,
3
3
3
of the
15
15
15
class sessions were lectures, while all others were devoted to fieldwork in parks. In the spring, the number of sessions devoted to fieldwork remained the same, but the total number of sessions increased to
18
18
18
. In the spring, what percent of class sessions were lectures?
\newline
Choose
1
1
1
answer:
\newline
(A)
16.7
%
16.7 \%
16.7%
\newline
(B)
33.3
%
33.3 \%
33.3%
\newline
(C)
66.7
%
66.7 \%
66.7%
\newline
(D)
83.3
%
83.3 \%
83.3%
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In a college philosophy class during the fall semester, there were
323
323
323
students.
42
%
42 \%
42%
of the students were philosophy majors, and the rest were not philosophy majors. In the spring semester, the same number of students who were not philosophy majors were in the class as in the fall, but there were only
298
298
298
total students in the class. In the spring, what percent of students were not philosophy majors?
\newline
Choose
1
1
1
answer:
\newline
(A)
46
%
46 \%
46%
\newline
(B)
58
%
58 \%
58%
\newline
(C)
63
%
63 \%
63%
\newline
(D)
92
%
92 \%
92%
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On Monday, a fruit vendor bought
80
80
80
pieces of fruit to sell at her market,
35
%
35 \%
35%
of which were apples and the rest of which were oranges. On Tuesday, the vendor bought the same number of oranges, but she only bought
73
73
73
pieces of fruit. What percentage of the fruit she bought on Tuesday was apples?
\newline
Choose
1
1
1
answer:
\newline
(A)
28.8
%
\mathbf{2 8 . 8 \%}
28.8%
\newline
(B)
38.3
%
38.3 \%
38.3%
\newline
(C)
65.0
%
65.0 \%
65.0%
\newline
(D)
71.2
%
71.2 \%
71.2%
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N
=
500
(
2.3
)
t
12
N=500(2.3)^{\frac{t}{12}}
N
=
500
(
2.3
)
12
t
\newline
The number of hits,
N
N
N
, a new website obtains
t
t
t
months after it is launched is modeled by the equation shown. By what percent does the number of hits grow in one year?
\newline
(Ignore the
%
\%
%
symbol when entering your answer. For example, if the answer is
11.2
%
11.2 \%
11.2%
, enter
11
11
11
.
2
2
2
.)
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We want to solve the following system of equations.
\newline
{
y
=
4
x
(
x
−
2
)
x
+
y
=
2
\left\{\begin{array}{l} y=4 x(x-2) \\ x+y=2 \end{array}\right.
{
y
=
4
x
(
x
−
2
)
x
+
y
=
2
\newline
One of the solutions to this system is
(
2
,
0
)
(2,0)
(
2
,
0
)
.
\newline
Find the other solution.
\newline
Your answer must be exact.
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We want to solve the following system of equations.
\newline
{
x
2
+
y
2
=
1
y
=
2
x
+
2
\left\{\begin{array}{l} x^{2}+y^{2}=1 \\ y=2 x+2 \end{array}\right.
{
x
2
+
y
2
=
1
y
=
2
x
+
2
\newline
One of the solutions to this system is
(
−
1
,
0
)
(-1,0)
(
−
1
,
0
)
.
\newline
Find the other solution. Your answer must be exact.
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