Paul and Ryan earned $3 an hour. Paul worked 5 hours more than Ryan. They earned $105 together. What is, x, the number of hours Ryan worked?

Question

Paul and Ryan earned $3 an hour. Paul worked 5 hours more than Ryan. They earned $105 together. What is, x, the number of hours Ryan worked?

Answer 1

Hi Cayden,

 

This is a system of equations problem.

 

The problem tells us Paul worked 5 more hours then Ryan. Lets represent Paul by the variable p and Ryan will be variable x because that's what the problem wants us to use.

 

If Paul worked 5 more hours then Ryan we have the equation

p=5+x

 

The problem also says that Paul and Ryan earned $3 an hour and made $105. This can be written as,

 

3(p+x)=105

 

We can solve the equations for p and x.

 

p=5+x

3(p+x)=105

 

Because the first equation has isolated a variable lets plug that into the second equation,

 

3(5+x+x)=105

3(5+2x)=105

15+6x=105

6x=90

x=15

 

Thus, Ryan worked 15 hours.