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Math Problems
Grade 8
Multi-step word problems
A waitress sold
20
20
20
ribeye steak dinners and
12
12
12
grilled salmon dinners, totaling
$
573.12
\$ 573.12
$573.12
on a particular day. Another day she sold
26
26
26
ribeye steak dinners and
6
6
6
grilled salmon dinners, totaling
$
582.07
\$ 582.07
$582.07
. How much did each type of dinner cost?
\newline
The cost of ribeye steak dinners is
$
\$
$
□
\square
□
and the cost of salmon dinners is
$
\$
$
□
\square
□
. (Simplify your answer. Round to the nearest hundredth as needed.)
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A
40
40
40
milliliter
(
m
L
)
(\mathrm{mL})
(
mL
)
bottle of pre-diluted tea tree oil contains a
5
%
5 \%
5%
concentration of the active ingredient. If the seller charges
$
14.96
\$ 14.96
$14.96
for the total amount of active ingredient in the bottle, what is the price per
m
L
\mathrm{mL}
mL
of the active ingredient?
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A waitress sold
13
13
13
ribeye steak dinners and
26
26
26
grilled salmon dinners, totaling
$
569.37
\$ 569.37
$569.37
on a particular day. Another day she sold
26
26
26
ribeye steak dinners and
13
13
13
grilled salmon dinners, totaling
$
582.68
\$ 582.68
$582.68
. How much did each type of dinner cost?
\newline
The cost of ribeye steak dinners is
$
\$
$
□
\square
□
and the cost of salmon dinners is
$
\$
$
□
\square
□
.
\newline
(Simplify your answer. Round to the nearest hundredth as needed.)
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A waitress sold
18
18
18
ribeye steak dinners and
12
12
12
grilled salmon dinners, totaling
$
563.44
\$ 563.44
$563.44
on a particular day. Another day she sold
26
26
26
ribeye steak dinners and
6
6
6
grilled salmon dinners, totaling
$
580.72
\$ 580.72
$580.72
. How much did each type of dinner cost?
\newline
The cost of ribeye steak dinners is
$
\$
$
□
\square
□
and the cost of salmon dinners is
$
\$
$
□
\square
□
. (Simplify your answer. Round to the nearest hundredth as needed.)
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Yuki works at an aquarium. To clean a tank, she calculates
7
900
\frac{7}{900}
900
7
of the tank's total volume, and she adds that much cleaning solution to the tank. For a certain tank, this works out to be
2
1
3
2\frac{1}{3}
2
3
1
L
L
L
of cleaning solution.
\newline
What is the total volume of the tank?
\newline
□
\square
□
liters
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One cookbook recommends that a person can substitute
1
Tbsp
1\,\text{Tbsp}
1
Tbsp
of dried mint leaves for
1
4
\frac{1}{4}
4
1
c
c
c
of fresh mint leaves. The salad recipe calls for
2
Tbsp
2\,\text{Tbsp}
2
Tbsp
of fresh mint leaves. How many
Tbsp
\text{Tbsp}
Tbsp
of dried mint leaves could a person substitute into the recipe? (There are
16
Tbsp
16\,\text{Tbsp}
16
Tbsp
in
1
c
1\,\text{c}
1
c
.)
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Marco's mom gave him
d
d
d
dollars for his allowance one week. He also earned
(
$
14.55
)
(\$14.55)
(
$14.55
)
for his newspaper route that week.
\newline
How much money does Marco have?
\newline
Write your answer as an expression.
\newline
□
\square
□
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The chambered nautilus is a deepsea creature with a spiral shell that can withstand pressure up to
1180
1180
1180
pounds per square inch (
psi
\text{psi}
psi
). Underwater pressure consists of atmospheric pressure, which is
14.7
psi
14.7\text{psi}
14.7
psi
, plus
0.45
psi
0.45\text{psi}
0.45
psi
of hydrostatic pressure per foot of depth under water. To the nearest foot, what is the maximum depth under water at which the shell of a chambered nautilus can withstand the pressure?
\newline
□
\square
□
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Some friends are planning to make a neighborhood garden. The total area available for the garden is
210
square meters
210\,\text{square meters}
210
square meters
, and they want this to be
1
1
3
1\frac{1}{3}
1
3
1
times the area of the plant beds in the garden.
\newline
What should the area of the plant beds be?
\newline
□
meters
\square\,\text{meters}
□
meters
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(
2
2
2
) Mrs. Katz bought
3
3
3
pounds of apples and a muffin for snacks. The apples cost
$
2.59
\$ 2.59
$2.59
per pound if you buy less than
3
3
3
pounds and
$
2.12
\$ 2.12
$2.12
per pound if you buy
3
3
3
or more pounds. The muffin cost
$
1.95
\$ 1.95
$1.95
. How much did she spend?
\newline
Answer: \$\(\newline\)\[ (3 \times 2.12) \]
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The ratio of Aiden to Daniel's savings was
4
:
5
4:5
4
:
5
at first. After Aiden saved another
$
138
\$138
$138
and Daniel saved another
$
39
\$39
$39
, Aiden had twice of Daniel's amount. How much did Aiden have in the end?
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8
8
8
. On a hot day in Brooks, a trucker loaded
37
00
‾
L
37 \underline{00} \mathrm{~L}
37
00
L
of diesel fuel. He then drove to Whitehorse, where the temperature was
23.0
K
23.0 \mathrm{~K}
23.0
K
lower than Brooks, and delivered the entire load. How many liters of diesel fuel did he deliver?
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One summer a football camp orders
40
40
40
footballs from a website. Including the one-time shipping fee, the total cost is
$
685
\$ 685
$685
. The next year the camp orders
70
70
70
footballs for the same website and pays
$
1135
\$ 1135
$1135
including the same shipping fee.
\newline
What is the cost per football?
\newline
Submit
\newline
What is the one-time shipping fee?
\newline
Submit
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4
4
4
A rectangular door sign has an area of
577
577
577
.
6
6
6
square centimeters. The length of the sign is
38
38
38
centimeters. What is its width?
\newline
The Wid Width
\newline
e bought a skateboard for
$
98.91
\$ 98.91
$98.91
. This is
3
3
3
times
h
h
h
as the cost of the helmet he bought. What is t of the helmet?
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Paolo helped in the community garden for
2
3
4
2\frac{3}{4}
2
4
3
hours this week. That was
1
5
6
1\frac{5}{6}
1
6
5
equal-length shifts, because Paolo stopped early one day when it started to rain. How long is a single shift?
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After it snows, it takes Maria and her little sister Anita
1
2
\frac{1}{2}
2
1
of an hour to shovel the snow off of the sidewalks on their street. This is
2
3
\frac{2}{3}
3
2
of the time it takes Maria to do the same job by herself. How long does it take Maria do this job by herself?
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For the past ext{
26
26
26
} years, Eric has contributed ext{ extdollar
630
630
630
} to his RRSP at the beginning of every month. The plan earned ext{
7
7
7
.
30
30
30
ext{ extpercent}} compounded annually for the first ext{
14
14
14
} years and ext{
8
8
8
ext{ extpercent}} compounded monthly for the subsequent ext{
12
12
12
} years. What is the value of his RRSP today? Assume Eric did not make a payment today. For full marks your answer(s) should be rounded to the nearest cent. RRSP value =
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Jerry has a large car which holds
22
22
22
gallons of fuel and gets
20
20
20
miles per gallon. Kate has a smaller car which holds
16.5
16.5
16.5
gallons of fuel and gets
30
30
30
miles per gallon. If both cars have a full tank of fuel now and drive the same distance, in how many miles will the remaining fuel in each tank be the same?
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The chambered nautilus is a deep-sea creature with a spiral shell that can withstand pressure up to
1180
1180
1180
pounds per square inch. Underwater pressure consists of atmospheric pressure, which is
14.7
psi
14.7 \, \text{psi}
14.7
psi
, plus
0.45
psi
0.45 \, \text{psi}
0.45
psi
of hydrostatic pressure per foot of depth under water. To the nearest foot, what is the maximum depth under water at which the shell of a chambered nautilus can withstand the pressure?
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If a store sold a toy set at
$
80
\$ 80
$80
, it would make a profit of
$
2700
\$ 2700
$2700
. If each toy set is sold at
$
40
\$ 40
$40
instead, the shop will make a loss of
$
900
\$ 900
$900
. How many toy sets are there? What is the cost price of each toy sets?
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One day, a vendor sold
58
58
58
hot dogs and
84
84
84
bratwursts for a total of
$
268.30
\$ 268.30
$268.30
. The next day, the vendor sold
44
44
44
hot dogs and
92
92
92
bratwursts for a total of
$
271.40
\$ 271.40
$271.40
. What is the cost of one hot dog and the cost of one bratwurst? If the Winchester family buys
3
3
3
hot dogs and
2
2
2
bratwursts, how much will they pay?
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A waitress sold
18
18
18
ribeye steak dinners and
12
12
12
grilled salmon dinners, totaling
$
563.44
\$ 563.44
$563.44
on a particular day. Another day she sold
26
26
26
ribeye steak dinners and
6
6
6
grilled salmon dinners, totaling
$
580.72
\$ 580.72
$580.72
. How much did each type of dinner cost?
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Some friends are planning to make a neighborhood garden. The total area available for the garden is
210
square meters
210 \, \text{square meters}
210
square meters
, and they want this to be
1
1
3
1 \frac{1}{3}
1
3
1
times the area of the plant beds in the garden. What should the area of the plant beds be?
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Noam had a length of
13
1
3
13 \frac{1}{3}
13
3
1
of ribbon and cut
3
1
3
3 \frac{1}{3}
3
3
1
equal-sized strips the full width of the ribbon. How long is each whole strip?
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Yuki works at an aquarium. To clean a tank, she calculates
7
900
\frac{7}{900}
900
7
of the tank's total volume, and she adds that much cleaning solution to the tank. For a certain tank, this works out to be
2
1
3
L
2 \frac{1}{3}L
2
3
1
L
of cleaning solution. What is the total volume of the tank?
\newline
_
_
_
_
_
liters
\_\_\_\_\_ \text{liters}
_____
liters
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Gavin drank
3
4
\frac{3}{4}
4
3
of the orange juice from a container, which was
3
8
\frac{3}{8}
8
3
of the orange juice originally in the container. How much orange juice was originally in the container?
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The population of a city increases by
4
%
4 \%
4%
per year. What should we multiply the current population by to find the next year's population in one step?
\newline
Answer:
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David invests money in an account paying a simple interest of
1
%
1 \%
1%
per year. If he invests
$
100
\$ 100
$100
and no money will be added or removed from the investment, how much will he have in one year, in dollars and cents?
\newline
Answer:
$
\$
$
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Maya spent
3
8
\frac{3}{8}
8
3
of her monthly allowance on books and then spent
$
12.50
\$12.50
$12.50
on a movie ticket. If she has
$
28.50
\$28.50
$28.50
left, how much was her monthly allowance?
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Piper owns a small business selling clothing. She knows that in the last week
47
47
47
customers paid cash,
9
9
9
customers used a debit card, and
4
4
4
customers used a credit card.
\newline
Based on these results, express the probability that the next customer will pay with a debit card as a fraction in simplest form.
\newline
Answer:
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i buy an old camera for
50
50
50
and sell it for
60
60
60
. i buy it again at
70
70
70
and finally sell it again at
80
80
80
. what is my profit.
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Sathish is going on a
2100
2100
2100
-kilometer road trip with
2
2
2
friends, whom he will pick up
150
150
150
kilometers after he begins the trip and drop off when there are
150
150
150
kilometers remaining. The car consumes
6
6
6
liters of gas for every
100
100
100
kilometers, and gas costs
$
1.20
\$ 1.20
$1.20
per liter.
\newline
Sathish will pay for all of the gas when he is alone in the car, but he and his friends will split the cost evenly when they are together.
\newline
How much will Sathish pay for gas?
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Mary is a scientist. Using a microscope, she looks at a salt crystal and discovers its shaped like a cube. Each square face has side length
0.1
mm
0.1\,\text{mm}
0.1
mm
. Draw the crystal's square face such that
1
1
1
unit on the grid below represents
0.01
mm
0.01\,\text{mm}
0.01
mm
.
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At Andy's Market, the price of a box of brand-name cereal is
1.5
1.5
1.5
times the price of a box of generic cereal. If the price of a box of brand-name cereal is
$
3.60
\$3.60
$3.60
, which of the following can be used to determine
x
x
x
, the price of a box of generic cereal in dollars?
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A waitress sold
10
10
10
ribeye steak dinners and
10
10
10
grilled salmon dinners, totaling
$
584.01
\$584.01
$584.01
on a particular day. Another day she sold
11
11
11
ribeye steak dinners and
5
5
5
grilled salmon dinners, totaling
$
584.45
\$584.45
$584.45
. How much did each type of dinner cost?
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A book sold
35
,
600
35,600
35
,
600
copies in its first month of release. Suppose this represents
6.1
%
6.1\%
6.1%
of the number of copies sold to date. How many copies have been sold to date? Round your answer to the nearest whole number.
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A party mix is made by adding nuts that sell for
$
2.50
\$2.50
$2.50
per kg to a cereal mixture that sells for
$
1
\$1
$1
per kg. How much of each should be added to obtain
60
60
60
kg of a mix that will sell for
$
2.10
\$2.10
$2.10
per kg?
\newline
\newline
Number of
\newline
kilograms
\newline
\newline
Price per
\newline
kilogram
\newline
(in dollars)
\newline
\newline
Values
\newline
(in dollars)
\newline
\newline
Nuts
\newline
x
x
x
\newline
2.50
2.50
2.50
\newline
\newline
Cereal
\newline
y
y
y
\newline
1.00
1.00
1.00
\newline
\newline
Mixture
\newline
2.10
2.10
2.10
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A waitress sold
11
11
11
ribeye steak dinners and
33
33
33
grilled salmon dinners, totaling
$
580.27
\$580.27
$580.27
on a particular day. Another day she sold
30
30
30
ribeye steak dinners and
11
11
11
grilled salmon dinners, totaling
$
580.58
\$580.58
$580.58
. How much did each type of dinner cost?
\newline
The cost of ribeye steak dinners is
$
□
\$\square
$
□
and the cost of salmon dinners is
$
□
\$\square
$
□
.
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You need to rent a moving truck for a day. You have identified two companies that rent trucks. Company A charges
$
50
\$50
$50
per day plus
$
0.25
\$0.25
$0.25
per mile. Company B charges
$
35
\$35
$35
per day plus
$
0.30
\$0.30
$0.30
per mile. For how many miles will the cost of renting be the same?
miles
\text{ miles}
miles
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You need to rent a moving truck for a day. You have identified two companies that rent trucks. Company A charges
$
50
\$ 50
$50
per day plus
$
0.25
\$ 0.25
$0.25
per mile. Company
B
B
B
charges
$
35
\$ 35
$35
per day plus
$
0.30
\$ 0.30
$0.30
per mile For how many miles will the cost of renting be the same?
\newline
_
_
_
_
_
\_\_\_\_\_
_____
miles
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Avi and Micah are teammates on a track and field team. Avi's best long jump is
1
1
6
1\frac{1}{6}
1
6
1
times as long as Micah's. Avi's best long jump is
3
1
2
3\frac{1}{2}
3
2
1
meters. How long is Micah's best long jump?
meters
\text{meters}
meters
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A grocery store charges
$
3.02
\$ 3.02
$3.02
per milk jug and
$
0.10
\$ 0.10
$0.10
per grocery bag. You never buy the bags because you bring your own.
\newline
Is the total price you pay proportional to the number of milk jugs you buy?
\newline
Choose
1
1
1
answer:
\newline
(A) Yes
\newline
(B) No
\newline
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Damian is working two summer jobs, making
$
12
\$ 12
$12
per hour babysitting and making
$
6
\$ 6
$6
per hour walking dogs. In a given week, he can work a maximum of
17
17
17
total hours and must earn a minimum of
$
150
\$ 150
$150
. If Damian worked
5
5
5
hours walking dogs, determine the maximum number of whole hours babysitting that he can work and still meet his requirements.
\newline
Answer:
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Idil has some dimes and some quarters. She has no less than
18
18
18
coins worth no more than
$
3.60
\$ 3.60
$3.60
combined. If Idil has
8
8
8
dimes, determine the maximum number of quarters that she could have.
\newline
Answer:
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Many bank accounts never go below zero. But some banks will allow a negative balance, at least for a short time, called an overdraft. It means someone has taken out, or 'drafted', more money than was in the account to begin with. Hunter's account went into overdraft. To get back to a positive balance, he deposited money at a steady rate of
$
24.21
\$ 24.21
$24.21
per week. After
3
3
3
weeks, he had
$
13.25
\$ 13.25
$13.25
in the account. What was the balance when the account went into overdraft?
\newline
Answer:
$
\$
$
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Many bank accounts never go below zero. But some banks will allow a negative balance, at least for a short time, called an overdraft. It means someone has taken out, or 'drafted', more money than was in the account to begin with. Arun's account has gone into overdraft. His balance is
$
−
34.33
\$-34.33
$
−
34.33
. To get back to a positive balance, he plans to deposit money at a steady rate of
$
28.98
\$ 28.98
$28.98
per week. How much will be in his account after
6
6
6
weeks?
\newline
Answer:
$
\$
$
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Grace examines two different size bottles of the same laundry detergent. The price for the
100
100
100
ounce bottle is
$
9.99
\$9.99
$9.99
and the price for the
150
150
150
-ounce bottle is
$
12.99
\$12.99
$12.99
. How much money will Grace save per
100
100
100
ounces if she purchases the larger bottle?
\newline
Choose
1
1
1
answer:
\newline
(A)
$
0.01
\$0.01
$0.01
\newline
(B)
$
1.33
\$1.33
$1.33
\newline
(C)
$
2.00
\$2.00
$2.00
\newline
(D)
$
8.66
\$8.66
$8.66
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