Write System of Equations from Context

Question

Riley and Jace work at a dry cleaners ironing shirts. Riley can iron 25 shirts per hour, and Jace can iron 30 shirts per hour. Riley worked 3 more hours than Jace and they ironed 460 shirts between them. Write a system of equations that could be used to determine the number of hours Riley worked and the number of hours Jace worked. Define the variables that you use to write the system.

I need

Let __=_______________________

Let __=_______________________

and

The Systems of Equations

____________________

____________________

Answer 1

Let R = the number of hours Riley worked.

Let J = the number of hours Jace worked.

Write an equation for the number of hours worked based on information related to time in the word problem: "Riley worked 3 hours more than Jace."

R = 3 + J

For example, if Jace worked 6 hours, then Riley worked 9 hours. Substituting my own numbers I can check that if J=6, then R=9. Some students will incorrectly add 3 to Riley's hours. But Riley's hours should always be greater than Jace's hours based on information in the word problem.

Next, make a relation to the number of shirts produced. One thing to notice is we don't know how many shirts Riley and Jace ironed and our variables do not solve for the number of shirts. The variables solve for the number of hours each person worked. There is information about the rate that each person worked: "Riley can iron 25 shirts per hour, and Jace can iron 30 shirts per hour."

To write an expression for the number of shirts ironed, multiply each person's (hourly rate) x (# hours worked):

# shirts Riley ironed = (Riley's rate per hour) x (the number of hours Riley worked)

= 25R

# shirts Jace ironed = (Jace's rate per hour) x (the number of hours Jace worked)

= 30J

Together, the two of them ironed a total of 460 shirts. To show that, add the two expressions together and set equal to 460.

25R + 30J = 460