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Math Problems
Grade 8
Percent of change
I have a cockroach problem in my living room. Don't ask how, but I counted
64
64
64
cockroaches today. And they are growing at a rate of
25
%
25 \%
25%
every day.
\newline
How many cockroaches do you think I'll have after three days?
\newline
□
\square
□
cockroaches
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Caleb bought groceries and paid
$
1.60
\$1.60
$1.60
in sales tax. The sales tax rate is
2.5
%
2.5\%
2.5%
. Caleb bought groceries and paid in sales tax. The sales tax rate is. Caleb bought groceries and paid in sales tax. The sales tax rate is. Caleb bought groceries and paid in sales tax. The sales tax rate is. Caleb bought groceries and paid in sales tax. The sales tax rate is. Caleb bought groceries and paid in sales tax. The sales tax rate is. Caleb bought groceries and paid in sales tax. The sales tax rate is.
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the greens brought a condo for
$
110
,
000
\$110,000
$110
,
000
in
2005
2005
2005
.If its value appreciates at
6
%
6\%
6%
per year,what will the value be in
2012
2012
2012
?
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Kong took
15
%
15 \%
15%
fevrer seconds than Nalan toole to che multiplication fimed test Komis took ef
5
5
5
sectidh
\newline
How many seconds did Molan take?
\newline
\qquad
seconds
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Keith and his friends are heading to the Thunder Beach water park. They plan to purchase the group package, which costs
$
78
\$78
$78
for
6
6
6
people. That's
$
3
\$3
$3
less per person than the normal cost for an individual. What is the normal cost for an individual?
\newline
$
\$
$
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Grandpa Ernie is shrinking! Over the past
n
n
n
years, his height decreased by a total of
h
h
h
. It decreased by the same amount each year. What was the change in Grandpa Ernie's height each year?
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PERCENT OF CHANGE
\newline
Use your understonding of percent of change to answer the questions below
\newline
Marco is diseussing how prices have changed with his son, Paul. Paul does not believe him, so they decide to researeh the price of their favorite food items. Use the information to determine the percent change in questions
1
−
4
1-4
1
−
4
.
\newline
1
1
1
. What is the percent of change in the cost of a pizza?
\newline
2
2
2
. What is the percent of change in the cost of a cheeseburger?
\newline
3
3
3
. What is the percent of change in the cost of a serving of fries?
\newline
4
4
4
. What is the percent of change in the cost of a hot dog?
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After the outbreak of a mysterious disease, the average wait time at a hospital increased by
70
%
70\%
70%
. Before the outbreak, the average wait time at the hospital was
m
m
m
minutes.
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The angle of a sector is decreased by
20
%
20\%
20%
but its radius is increased by
x
%
x\%
x
%
. If the arc length of the sector remains unchanged, find the value of
x
x
x
.
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roblem
7
7
7
:
\newline
An investor has an account with stock from two different companies. Last year, his stock in Company A was worth
$
5260
\$ 5260
$5260
and his stock in Company B was worth
$
390
\$ 390
$390
The stock in Company A has increased
25
25
25
\% since last year and the stock in Compar B has increased
6
%
6 \%
6%
. What was the total percentage increase in the investor's stock account? Round your answer to the nearest tenth (if necessary).
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An investor has an account with stock from two different companies. Last year, his stock in Company A was worth
$
2450
\$ 2450
$2450
and his stock in Company B was worth
$
2400
\$ 2400
$2400
. The stock in Company A has increased
6
6
6
\% since last year and the stock in Company B has increased
3
%
3 \%
3%
. What was the total percentage increase in the investor's stock account? Round your answer to the nearest tenth (if necessary).
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An investor has an account with stock from two different companies. Last year, his stock in Company A was worth
$
6260
\$ 6260
$6260
and his stock in Company B was worth
$
4650
\$ 4650
$4650
. The stock in Company A has decreased
20
%
20 \%
20%
since last year and the stock in Company B has decreased
4
%
4 \%
4%
. What was the total percentage decrease in the investor's stock account? Round your answer to the nearest tenth (if necessary).
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The tape diagram shows that Bol\'ivar takes
40
40
40
minutes to steam a batch of tamales. A tape diagram with one tape split into
5
5
5
equal parts. The first
2
2
2
parts are shaded. A curved brace above the first
2
2
2
parts is labeled
40
40
40
. A curved brace below the first
2
2
2
parts is labeled
100
100
100
percent. A tape diagram with one tape split into
5
5
5
equal parts. The first
2
2
2
parts are shaded. A curved brace above the first
2
2
2
parts is labeled
40
40
40
. A curved brace below the first
2
2
2
parts is labeled
100
100
100
percent. Complete the table to show different percentages of the steaming time. Time (
5
5
5
3
3
3
)
5
5
5
3
3
3
Percentage of of of
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An author published a book which was being sold online. The first month the author sold
27500
27500
27500
books, but the sales were declining steadily at
10
%
10 \%
10%
each month. If this trend continues, how many total books would the author have sold over the first
6
6
6
months, to the nearest whole number?
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Parker just started a running plan where he runs
16
16
16
miles the first week and then increases the number of miles he runs by
5
%
5\%
5%
each week. If he keeps up this plan for
5
5
5
weeks, how many total miles would Parker have run, to the nearest whole number?
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Vanessa earns a base salary of
400
400
400
every week with an additional
5
%
5\%
5%
commission on everything she sells. Vanessa sold
1650
1650
1650
worth of items last week. What was Vanessa's total pay last week?
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The double number line shows that Bira has ridden
28
28
28
on a , which is
80
%
80\%
80%
of a full rotation on the carousel.
28
28
28
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A swimming pool had
2
,
5
2,5
2
,
5
million liters of water in it. Some water evaporated, and the pen the pool only had
2
2
2
million liters of water in it. What percent of water evaporated?
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Write an algebraic equation for the following problem and then solve it.
\newline
A town's employment statistics show that
867
867
867
of its residents were unemployed last month. This is a decrease of
15
%
15 \%
15%
from the previous month. How many residents were unemployed in the previous month?
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The cost of a brand new car was
$
35000
\$ 35000
$35000
. After a year, its value dropped by
15
%
15 \%
15%
. If sold it at a loss of
$
3000
\$ 3000
$3000
, how much did I sell the car for?
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The cost of a brand new car was
$
35000
\$ 35000
$35000
. After a year, its value dropped by
15
%
15 \%
15%
.
1
1
1
.
1
1
1
sold it at a loss of
$
3000
\$ 3000
$3000
, how much did I sell the car for?
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The Orchard Ridge Zoo has a new red panda. The zoo's board of directors needs to pick a name for the panda and has narrowed down the list to three options. Each board member randomly surveys
20
20
20
zoo visitors to see which name is preferred. Here are the data from one board member's sample:
\newline
------- --
\newline
Rocky
13
13
13
\newline
Scarlet
6
6
6
\newline
Chili
1
1
1
\newline
------- --
\newline
What percentage of the zoo visitors in this sample prefer the name Rocky?
\newline
_____
%
\%
%
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The town of Crystal Palms is considering building a public swimming pool. The members of the town council each randomly survey
20
20
20
residents to see if there is enough support for the pool. Here are the data from one council member's survey, with Yes indicating support for the pool and No indicating no support:
\newline
--------- --
\newline
Yes
12
12
12
\newline
No
5
5
5
\newline
Undecided
3
3
3
\newline
--------- --
\newline
What percentage of those surveyed support building the swimming pool?
\newline
\newline
_
_
_
_
%
\_\_\_\_\%
____%
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What is the percent of change from
20
20
20
to
18
18
18
?
\newline
Choices:
\newline
(A)
9
%
9\%
9%
decrease
\newline
(B)
9
%
9\%
9%
increase
\newline
(C)
10
%
10\%
10%
increase
\newline
(D)
10
%
10\%
10%
decrease
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What is the percent of change from
15
15
15
to
18
18
18
?
\newline
Choices:
\newline
(A)
3
%
3\%
3%
decrease
\newline
(B)
20
%
20\%
20%
decrease
\newline
(C)
20
%
20\%
20%
increase
\newline
(D)
3
%
3\%
3%
increase
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What is the percent of change from
5
5
5
to
1
1
1
?
\newline
Choices:
\newline
(A)
4
%
4\%
4%
decrease
\newline
(B)
80
%
80\%
80%
decrease
\newline
(C)
80
%
80\%
80%
increase
\newline
(D)
4
%
4\%
4%
increase
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What is the percent of change from
8
8
8
to
10
10
10
?
\newline
Choices:
\newline
(A)
25
%
25\%
25%
decrease
\newline
(B)
2
%
2\%
2%
increase
\newline
(C)
2
%
2\%
2%
decrease
\newline
(D)
25
%
25\%
25%
increase
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What is the percent of change from
20
20
20
to
11
11
11
?
\newline
Choices:
\newline
(A)
45
%
45\%
45%
decrease
\newline
(B)
45
%
45\%
45%
increase
\newline
(C)
9
%
9\%
9%
decrease
\newline
(D)
9
%
9\%
9%
increase
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What is the percent of change from
34
34
34
to
17
17
17
?
\newline
Choices:
\newline
(A)
5
%
5\%
5%
decrease
\newline
(B)
5
%
5\%
5%
increase
\newline
(C)
50
%
50\%
50%
increase
\newline
(D)
50
%
50\%
50%
decrease
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What is the percent of change from
75
75
75
to
36
36
36
?
\newline
Choices:
\newline
(A)
52
%
52\%
52%
decrease
\newline
(B)
52
%
52\%
52%
increase
\newline
(C)
39
%
39\%
39%
increase
\newline
(D)
39
%
39\%
39%
decrease
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What is the percent of change from
50
50
50
to
31
31
31
?
\newline
Choices:
\newline
(A)
19
%
19\%
19%
increase
\newline
(B)
19
%
19\%
19%
decrease
\newline
(C)
38
%
38\%
38%
increase
\newline
(D)
38
%
38\%
38%
decrease
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What is the percent of change from
6
6
6
to
3
3
3
?
\newline
Choices:
\newline
(A)
3
%
3\%
3%
increase
\newline
(B)
50
%
50\%
50%
increase
\newline
(C)
3
%
3\%
3%
decrease
\newline
(D)
50
%
50\%
50%
decrease
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What is the percent of change from
20
20
20
to
30
30
30
?
\newline
Choices:
\newline
(A)
10
%
10\%
10%
increase
\newline
(B)
50
%
50\%
50%
decrease
\newline
(C)
50
%
50\%
50%
increase
\newline
(D)
10
%
10\%
10%
decrease
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What is the percent of change from
6
6
6
to
9
9
9
?
\newline
Choices:
\newline
(A)
50
%
50\%
50%
increase
\newline
(B)
3
%
3\%
3%
decrease
\newline
(C)
3
%
3\%
3%
increase
\newline
(D)
50
%
50\%
50%
decrease
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What is the percent of change from
46
46
46
to
23
23
23
?
\newline
Choices:
\newline
(A)
23
%
23\%
23%
decrease
\newline
(B)
23
%
23\%
23%
increase
\newline
(C)
50
%
50\%
50%
increase
\newline
(D)
50
%
50\%
50%
decrease
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What is the percent of change from
100
100
100
to
33
33
33
?
\newline
Choices:
\newline
(A)
74
%
74\%
74%
increase
\newline
(B)
67
%
67\%
67%
increase
\newline
(C)
74
%
74\%
74%
decrease
\newline
(D)
67
%
67\%
67%
decrease
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What is the percent of change from
10
10
10
to
7
7
7
?
\newline
Choices:
\newline
(A)
3
%
3\%
3%
increase
\newline
(B)
30
%
30\%
30%
decrease
\newline
(C)
3
%
3\%
3%
decrease
\newline
(D)
30
%
30\%
30%
increase
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Last year, wind turbines along a hilly ridge had an average output of
600
600
600
kilowatt hours per year. The turbines were upgraded, and now their average annual output is
73
%
73\%
73%
more. What is the new average yearly output?
\newline
____ kilowatt hours
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A local gym had
54
54
54
members last quarter. This quarter, with a change in its rates, it has
81
81
81
members. What is the percent of increase in the number of members?
\newline
_
_
_
_
%
\_\_\_\_\%
____%
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The last time it placed an order for ingredients, Sweet Treats Bakery ordered
6
,
730
6,730
6
,
730
kilograms of sugar. This time, the bakery is ordering
20
%
20\%
20%
more sugar. How much sugar is that?
\newline
____ kilograms
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Clean Machine is Seaside's premier house cleaning service. The company used
6
,
830
6,830
6
,
830
gallons of soap last year, and
50
%
50\%
50%
more than that this year. How many gallons of soap did the company use this year?
\newline
____ gallons
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In
2009
2009
2009
, Chloe paid
$
6
,
190
\$6,190
$6
,
190
in federal income tax. In
2010
2010
2010
, she paid
90
%
90\%
90%
more than in
2009
2009
2009
. How much did Chloe pay in
2010
2010
2010
?
\newline
$
\$
$
____
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Steve has run many marathons and keeps track of all of his finishing times. At a race last month, he finished in
260
260
260
minutes. At his next race, he finished with a time that was
20
%
20\%
20%
longer. What was his finishing time at the most recent race?
\newline
____ minutes
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A magician is training for an underwater escape trick. Upon first trying, she could hold her breath for
66
66
66
seconds. Now, using a different technique, she can hold it for
50
%
50\%
50%
longer. How long can the magician currently hold her breath?
\newline
_
_
_
_
\_\_\_\_
____
seconds
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Last year, a gardening store ordered
820
,
540
820,540
820
,
540
potted plants. This year, they ordered
1
,
517
,
999
1,517,999
1
,
517
,
999
potted plants. What is the percent of increase in the number of potted plants ordered annually?
\newline
_
_
_
_
%
\_\_\_\_\%
____%
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Dr. Lambert, a farm veterinarian, just weighed a pig and found out that it is
9
kilograms
9\,\text{kilograms}
9
kilograms
, which is
10
%
10\%
10%
less than the last time he checked. How much did the pig weigh last time?
\newline
____ kilograms
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This year, Tea Off served a total of
1
,
026
1,026
1
,
026
cups of chamomile tea to its customers. The manager notes that this number is
40
%
40\%
40%
lower than the last year. How many cups of chamomile tea did the cafe serve last year?
\newline
____ cups
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This year, Michael gave
234
234
234
piano performances. That is
40
%
40\%
40%
fewer than last year. How many times did Michael perform last year?
\newline
____ piano performances
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At the end of the year, cars made in the current year are marked down to make room for next year's models. One particular model has a sale price of
$
41
,
705
\$41,705
$41
,
705
, which is
5
%
5\%
5%
less than it sold for when it was new. What was the original price of the vehicle?
\newline
$
\$
$
____
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Pamela has been keeping an eye on an emerald ring she likes. She just noticed that it has been marked down to
$
18
,
284
\$18,284
$18
,
284
, which is
60
%
60\%
60%
less than its original price. What was the original price of the ring?
\newline
$
\$
$
____
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