Name: Date: Lesson 5.3 Real-World Problems: Systems
of Linear Equations
Solve using systems of linear equations.
1. Jenny purchased 26 magazines for her project research at a total cost of $134.
The art related magazines cost $4 each, while the science related magazines
cost $7 each. Find the number of art related magazines and science related
magazines purchased.
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2. A total of 95 theme park tickets were sold for $960. Each adult ticket cost $12
and each child’s ticket cost $9. Find the number of adult tickets and the number
of children’s tickets sold.
3. Adam bought 5 packets of roasted peanuts and 3 packets of beef jerky for
$37.80. Joe bought 3 packets of roasted peanuts and 2 packets of beef jerky
for $23.87. Find the cost of a packet of roasted peanuts and a packet of
beef jerky.
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4. Half a dozen glass containers and 2 plastic containers can store up to 180 wheat
crackers. Four glass containers can store a total of 25 more wheat crackers than
5 plastic containers. How many wheat crackers can each glass container and each
plastic container store?
5. The diagram shows an equilateral trianglar face of a crystal solid with the given
sides. Find the values of x and y.
36 cm
(10x 7y) cm
6. Mrs. Quincy plans to build a rectangular sandbox for her grandson. She has
26 meters of wood for the perimeter of the sandbox. The length of the sandbox
is to be 3 meters longer than the breadth.
a)Write a system of linear equations relating the length l and width w of the
perimeter of the sandbox.
b)Find the dimensions of the rectangular sandbox.
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(6x 3y) cm
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7. A vending machine only accepts dimes and quarters. There are 85 coins
in the machine with a total value of $16.75. How many of each coin are in
the machine?
8. At a fund raising event, a booth was set up to sell handmade cards and photo
frames. On the first day, 3 cards and 9 photo frames were sold for a total of $75.
The next day, 8 cards and 5 photo frames were sold for a total of $67.
Find the selling price of a card and the selling price of a photo frame.
9. Ben took a mathematics quiz where he had to solve the following questions.
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a)The sum of two numbers is 31. Twice the larger number is 7 more than
3 times the smaller number. What are the numbers?
b)The sum of a number and twice a second number is 14. When the second
number is subtracted from the first number, the difference is 2. Find the
two numbers.
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10. A tennis club charges an entry fee for the players at the club. The table below
shows the money received on a particular Saturday and Sunday.
Day
Number
of Senior
Players
Number
of Junior
Players
Saturday
35
20
Sunday
55
45
Entry Fees
Charged ($)
For
Seniors
For
Juniors
x
y
Amount of Money
Received ($)
310
555
How much is the entry fee for each senior and each junior?
Font Size
Number of Words on a Page
Small
1,150
Large
850
Jacob needs to print a document with a total of 12,600 words on exactly
12 pages. Find the number of pages in the document that should be printed
in small font and the number of pages that should be printed in large font.
12. Kelly, a chemist, was asked to prepare 24 gallons of a solution that is 50% acidic
by mixing a solution that is 20% acidic with another solution that is 70% acidic.
How much of each solution should she use?
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11. The table shows the number of words that can be printed on a page for two
given font sizes.
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