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Math Problems
Grade 8
Multi-step word problems
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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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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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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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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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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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 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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