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Math Problems
Grade 8
Solve a system of equations using substitution: word problems
Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.
\newline
Ben and his cousin Rachel are picking apples in their grandparents' orchard. Ben has filled
8
8
8
baskets with apples and is filling them at a rate of
5
5
5
baskets per hour. Rachel has
11
11
11
full baskets and will continue picking at
2
2
2
baskets per hour. Once the cousins get to the point where they have filled the same number of baskets, they will carry them to the barn and then eat lunch. How long will that take? How much fruit will they have picked by then?
\newline
In
_
_
\_\_
__
hours, the cousins will each have filled
_
_
\_\_
__
baskets with apples.
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Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.
\newline
Vicky and Diana each opened a savings account on the same day. Vicky started by putting
$
404
\$404
$404
in her account, and she will deposit an additional
$
188
\$188
$188
each week. Diana made an initial deposit of
$
442
\$442
$442
, and she will add
$
186
\$186
$186
more each week. Eventually, Vicky and Diana will each have the same amount saved. What is that amount? How many weeks will that take?
\newline
Vicky and Diana will each have saved a total of
$
\$
$
_____ after _____ weeks.
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Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.
\newline
Peter and Francesca just had business cards made. Peter's printing company charged a one-time setup fee of
$
14
\$14
$14
and then
$
8
\$8
$8
per box of cards. Francesca, meanwhile, ordered hers online. They cost
$
6
\$6
$6
per box. There was no setup fee, but she had to pay
$
16
\$16
$16
to have her order shipped to her house. By coincidence, Peter and Francesca ended up spending the same amount on their business cards. How much did each spend? How many boxes did each buy?
\newline
Peter and Francesca each spent
$
\$
$
_____ on business cards, buying _____ boxes.
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Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.
\newline
Leroy, a frequent business traveler, is considering signing up for a hotel rewards program. Hotel Elegance is currently offering
648
648
648
points for signing up, plus
24
24
24
points for every night Leroy books at the hotel. Alternatively, Hotel Paradiso is offering a sign-up bonus of
412
412
412
points, plus
83
83
83
points per night. If Leroy books a certain number of nights, the points he earns with either hotel will be the same. How many nights will that be? How many points will he have?
\newline
If he books nights, he will earn points at either hotel.
\newline
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Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.
\newline
Dwayne and his little brother made up a game using coins. They flip the coins towards a cup and receive points for every one that makes it in. Dwayne starts with
20
20
20
points, and his little brother starts with
17
17
17
points. Dwayne gets
1
1
1
point for every successful shot, and his brother, since he is younger, gets
4
4
4
points for each successful shot. Eventually, the brothers will have a tied score in the game. How many additional shots will each brother have made? How many points will they both have?
\newline
Dwayne and his brother will have each made
_
_
_
_
\_\_\_\_
____
shots, for a tied score of
_
_
_
_
\_\_\_\_
____
.
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Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.
\newline
Kate, an office manager, needs to find a courier to deliver a package. The first courier she is considering charges a fee of
$
14
\$14
$14
plus
$
1
\$1
$1
per pound. The second charges
$
13
\$13
$13
plus
$
2
\$2
$2
per pound. Kate determines that, given her package's weight, the two courier services are equivalent in terms of cost. What is the weight? How much will it cost?
\newline
At a package weight of
_
_
\_\_
__
pounds, the two couriers both cost
$
_
_
_
_
_
_
\$\_\_\_\_\_\_
$______
.
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Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.
\newline
Mrs. Warren, the P.E. teacher, is pairing off students to race against each other. Colton can run
5
5
5
yards per second, and Eduardo can run
9
9
9
yards per second. Mrs. Warren decides to give Colton a head start of
8
8
8
yards since he runs more slowly. Once the students start running, Eduardo will quickly catch up to Colton. How far will Eduardo have to run? How long will that take?
\newline
Eduardo will catch up to Colton after running
_
\_
_
yards in
_
\_
_
seconds.
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Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.
\newline
Fred, an office manager, needs to find a courier to deliver a package. The first courier he is considering charges a fee of
$
10
\$10
$10
plus
$
3
\$3
$3
per pound. The second charges
$
15
\$15
$15
plus
$
2
\$2
$2
per pound. Fred determines that, given his package's weight, the two courier services are equivalent in terms of cost. What is the weight? How much will it cost?
\newline
At a package weight of
‾
\underline{\quad}
pounds, the two couriers both cost
$
‾
\$\underline{\quad}
$
.
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Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.
\newline
Zane went to play miniature golf on Monday, when it cost
$
16
\$16
$16
to rent the club and ball, plus
$
1
\$1
$1
per game. Omar went Thursday, paying
$
2
\$2
$2
per game, plus rental fees of
$
6
\$6
$6
. By coincidence, they played the same number of games for the same total cost. How much did each one spend? How many games did each one play?
\newline
Zane and Omar each spent
$
\$
$
_____ and played _____ games.
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Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.
\newline
Felix and his good buddy Gavin are both mechanics at a shop that does oil changes. They are in a friendly competition to see who can complete the most oil changes in one day. Felix has already finished
6
6
6
oil changes today, and can complete more at a rate of
1
1
1
oil change per hour. Gavin just came on shift, and can finish
3
3
3
oil changes every hour. Sometime during the day, the friends will be tied, with the same number of oil changes completed. How long will that take? How many oil changes will Felix and Gavin each have done?
\newline
In
_
\_
_
hours, both men will have completed
_
\_
_
oil changes.
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Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.
\newline
Two rental car companies are running specials this month. At Manuel's Rentals, customers will pay
$
45
\$45
$45
to rent a mid-sized car for the first day, plus
$
13
\$13
$13
for each additional day. At Wildgrove Rent-a-Car, the price for a mid-sized car is
$
46
\$46
$46
for the first day and
$
12
\$12
$12
for every additional day beyond that. At some point, renting from either one of the companies would cost a customer the same amount. How much would the customer pay? How many additional days would that take?
\newline
The customer would pay
$
\$
$
_____ either way for _____ additional days.
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Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.
\newline
Students in Mrs. Russell's third grade class are working on times tables, and they demonstrate mastery by passing tests. Madelyn has passed
1
1
1
test so far. Her classmate, Quinn, has passed
7
7
7
tests of them. From now on, Madelyn plans to take and pass
2
2
2
tests per week. Meanwhile, Quinn plans to do
1
1
1
per week. At some point, Madelyn will catch up to Quinn. How long will it take? How many tests will each child have passed?
\newline
In
_
\_
_
weeks, the children will each have passed
_
\_
_
tests.
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Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.
\newline
Last Wednesday, two friends met up after school to read the book they were both assigned in Literature class. Maya can read
2
2
2
pages per minute, and she had already read
87
87
87
pages. Ariel, who has a reading speed of
4
4
4
pages per minute, had read
9
9
9
pages. Eventually they had read the same number of pages. How long did that take? How many pages had each of them read?
\newline
After
_
_
\_\_
__
minutes, Maya and Ariel had each read
_
_
\_\_
__
pages.
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Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.
\newline
Two classmates got together over the weekend to do their assigned History reading. Josiah can read
1
1
1
page per minute, while Edward can read
4
4
4
pages per minute. When they met, Josiah had already read
97
97
97
pages, and Edward had already gotten through
13
13
13
pages. After a while, they had both read the same number of pages. How long did that take? How many pages had each one read?
\newline
After
_
\_
_
minutes, Josiah and Edward had each read
_
\_
_
pages.
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Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.
\newline
Last Wednesday, two friends met up after school to read the book they were both assigned in Literature class. Bert can read
1
1
1
page per minute, and he had already read
79
79
79
pages. Preston, who has a reading speed of
3
3
3
pages per minute, had read
9
9
9
pages. Eventually they had read the same number of pages. How long did that take? How many pages had each of them read?
\newline
After
_
\_
_
minutes, Bert and Preston had each read
_
\_
_
pages.
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Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.
\newline
Felipe and Philip started out at their houses and are biking towards each other. Felipe started out first, and has already gone
5
5
5
kilometers. He bikes at a constant speed of
6
6
6
kilometers per hour. Philip just left, and rides at
7
7
7
kilometers per hour. When the boys meet halfway between their houses, they will continue to the park together. How far will each boy have ridden? How long will that take?
\newline
Felipe and Philip will have each biked
_
\_
_
kilometers in
_
\_
_
hours.
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Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.
\newline
Two classmates got together over the weekend to do their assigned History reading. Leo can read
1
1
1
page per minute, while Shawna can read
3
3
3
pages per minute. When they met, Leo had already read
75
75
75
pages, and Shawna had already gotten through
19
19
19
pages. After a while, they had both read the same number of pages. How many pages had each one read? How long did that take?
\newline
Leo and Shawna had each read
_
\_
_
pages after
_
\_
_
minutes.
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Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.
\newline
Mark and his cousin Leah are picking apples in their grandparents' orchard. Mark has filled
6
6
6
baskets with apples and is filling them at a rate of
4
4
4
baskets per hour. Leah has
12
12
12
full baskets and will continue picking at
3
3
3
baskets per hour. Once the cousins get to the point where they have filled the same number of baskets, they will carry them to the barn and then eat lunch. How much fruit will they have picked by then? How long will that take?
\newline
Mark and Leah will each have filled
_
_
\_\_
__
baskets in
_
_
\_\_
__
hours.
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Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.
\newline
Two students in Mr. Hoover's class, Bonnie and Hunter, have been assigned a workbook to complete at their own pace. They get together at Bonnie's house after school to complete as many pages as they can. Bonnie has already completed
35
35
35
pages and will continue working at a rate of
7
7
7
pages per hour. Hunter has completed
37
37
37
pages and can work at a rate of
6
6
6
pages per hour. Eventually, the two students will be working on the same page. How long will that take? How many pages will each of them have completed?
\newline
After
_
\_
_
hours, Bonnie and Hunter will have each completed
_
\_
_
pages in their workbooks.
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Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.
\newline
On the windowsill is a plant that is
19
19
19
inches tall. It is growing
2
2
2
inches per week. A second plant, which is
20
20
20
inches tall, is on the coffee table. It is growing
1
1
1
inch per week. Eventually the two plants will be the same height. How tall will the plants be? How many weeks will that take?
\newline
Each plant will be
_
\_
_
inches tall after
_
\_
_
weeks.
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Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.
\newline
Yesterday, two friends went into a bank to open savings accounts. Anita started by putting
$
826
\$826
$826
in her account, and she will deposit an additional
$
45
\$45
$45
each week. Felipe made no initial deposit, but he will add
$
104
\$104
$104
more each week. In a few weeks, the friends will have the same account balance. How many weeks will that take? What is that account balance?
\newline
In
_
_
_
\_\_\_
___
weeks, Anita and Felipe will each have an account balance of
$
_
_
_
_
_
\$\_\_\_\_\_
$_____
.
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Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.
\newline
Haley is looking for a job cutting hair. One option is self-employment at The Oakdale Salon, where she would pay
$
642
\$642
$642
per month to rent a station and keep all of her earnings. Another option is to work at a franchise, where she would just have to pay the salon
$
6
\$6
$6
for every haircut. If she performed a certain number of haircuts every month, the amount paid to either salon would be the same. How many haircuts would that be? How much would Haley pay?
\newline
If Haley performed _____ haircuts in a month, she would pay
$
\$
$
_____ to either salon.
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Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.
\newline
The Ferguson family is looking to rent a large truck for their upcoming move. With Rob's Moving, they would pay
$
8
\$8
$8
for the first day plus
$
9
\$9
$9
per additional day. With Clarksville Rent-a-Truck, in comparison, the family would pay
$
16
\$16
$16
for the first day plus
$
1
\$1
$1
per additional day. Before deciding on which company to use, Mrs. Ferguson wants to find out what number of additional days would make the two choices equivalent with regards to cost. How many additional days would that be? What would the total cost be?
\newline
If the Ferguson family rented the truck for ___ additional days, they would pay
$
\$
$
___ either way.
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