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Lesson: Solving Real-World Problems Using Systems of Linear Equations in Three Variables

Use the information in the problem to form equations using the variables. Once you have three equations and all three variables, and all three variables are represented, you can solve the problem. In this lesson, we will learn how to solve real-world problems using a system of linear equations in three variables.

Worksheet: Solving Real-World Problems Using Systems of Linear Equations in Three Variables • 16 Questions

Q1:

An animal shelter has a total of 350 animals comprised of cats, dogs, and rabbits. If the number of rabbits is 5 less than half the number of cats, and there are 20 more cats than dogs, how many of each are at the shelter?

A180 rabbits, 95 cats, 75 dogs
B70 rabbits, 150 cats, 130 dogs
C120 rabbits, 125 cats, 105 dogs
D78 rabbits, 146 cats, 126 dogs

Q2:

The sum of the ages of three brothers is 123 years. The first brother is 3 years older than the second brother who is 9 years older than the third. Find their current ages.

A37 years, 40 years, 46 years
B37 years, 46 years, 49 years
C34 years, 43 years, 46 years
D34 years, 37 years, 46 years
E34 years, 37 years, 43 years

Q3:

Three numbers sum up to 147. The smallest number is half the middle number, which is half the largest number. What are the three numbers?

Q4:

Three even numbers add up to 108. The smaller is half the larger and the middle number is of the larger. What are the three numbers?

A25, 33, 50
B30, 38, 40
C24, 36, 48
D20, 40, 48
E12, 18, 24

Q5:

If the size of one angle of a triangle is half the size of the second angle and less than the size of the third one by , then what are the sizes of the three angles?

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