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Lesson: Using Systems of Equations to Solve Problems

Many real-life situations can be modeled with equations. In this lesson, learn how to translate a real-life problem into a system of equations and to find its solution(s).

Worksheet: Using Systems of Equations to Solve Problems • 17 Questions

Q1:

A man’s age is 4 times his son’s age. In five years, the sum of their ages will be 105. How old are they now?

A21 years, 84 years
B25 years, 43 years
C19 years, 76 years
D20 years, 62 years
E23 years, 60 years

Q2:

Two cousins were born 8 years apart. How old will the elder be when the sum of their ages is equal to 20 years?

A16 years
B8 years
C14 years
D6 years
E12 years

Q3:

I am thinking of two numbers. Use the clues to determine what the numbers are.

The product of the two numbers is 48.
The difference between the two numbers is 2.

A7 and 5
B5 and 3
C8 and 6
D9 and 7
E6 and 4

Q4:

I am thinking of two numbers. Use the clues to determine what the numbers are.

When you divide one by the other, the quotient is 8.
The sum of the two numbers is 81.

A75 and 6
B4 and 8
C72 and 9
D71 and 10
E70 and 11

Q5:

A farmer finds there is a linear relationship between the number of bean stalks, , she plants and the yield, , each plant produces. When she plants 30 stalks, each plant yields 30 oz of beans. When she plants 34 stalks, each plant produces 28 oz of beans. Find a linear relationship in the form that gives the yield when stalks are planted.

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