Download Writing Systems of Equations from Word Problems

Writing Systems of Equations
from Word Problems
©2006, Mr. C. Burke
Sample Question
The difference in Chris’s and Dave’s ages is 9
years. The sum of their ages is 35. Chris is
older. Find both of their ages.
What are the key words?
Difference and sum
What are the two variables?
Chris’s age and Dave’s age.
Set up the equations
The difference in Chris’s and Dave’s ages is 9
years. The sum of their ages is 35. Chris is
older. Find both of their ages.
Let x = Chris’s age.
Let y = Dave’s age.
The difference of their ages.
x–y=9
The sum of their ages.
x + y = 35
Write the system and solve the
equations using elimination.
The difference in Chris’s and Dave’s ages is 9
years. The sum of their ages is 35. Chris is
older. Find both of their ages.
x–y=9
x + y = 35
2x
= 44
x
= 22
Use the value of x to find y.
22 + y = 35
22 – y = 9
y = 13
y = 13
ANSWER: Chris is 22 and Dave is 13.
Try this problem in your notebook.
There are 5 times as many boys as girls in a
school. The total number of boys and girls is
1500 students. How many boys and girls are
there in the school?
What are the variables?
What are the relationships between them?
What operations are being performed?
Did you come up with the right system
of equations?
There are 5 times as many boys as girls in a school.
The total number of boys and girls is 1500 students.
How many boys and girls are there in the school?
x = the number of girls
y = the number of boys
y = 5x
There are 5 times as many boys.
x + y = 1500 The total number in the school.
x + 5x = 1500
Use the substitution method.
Did you come up with the right system
of equations?
There are 5 times as many boys as girls in a school.
The total number of boys and girls is 1500 students.
How many boys and girls are there in the school?
x + 5x = 1500
Use the substitution method.
6x = 1500
x = 250
y = 5(250) = 1250
There are 250 girls and 1,250 boys.
Do these on your own. Write the
system of equations and solve.

Three shirts and a pair of pants cost $60.
Two shirts and two pairs of pants cost $70.
How much does each shirt cost?

A pet shop has eight more kittens than
puppies. The total number of kittens and
puppies is 36. How many kittens are there?
Do these on your own. Write the
system of equations and solve.

Lavaughn and Ani have a total of 130 CDs.
Lavaughn has 20 more than Ani. How many
CDs does Ani have?

The sum of two numbers is 41. Their
difference is 19. Find the bigger number.