Please explain and show work

Question

Kyle has two summer jobs. He earns 7.25 per hour at an icecream stand and 9.50 per hour doing landscaping. In July, Kyle will work 45 hours and earn 382.50. How many hours will Kyle do of landscaping? 

Answer 1

This is a systems of equations problem being that it has two statements made about two variables. We must set the variables first.

 

Let x = ice cream stand hours

Let y = landscaping hours 

 

Write the sentences based on the problem. First, Kyle works 45 hours total. 

 

x + y = 45

 

Kyle earns $382.50 total.

 

7.25x + 9.50y = 382.50

 

Solve for x and y. First, we must multiply one of the equationsfactor number so that one of the coefficients in front of one of the variables matches. So we'll multiply the first equation by 7.25.

 

7.25x + 7.25y = 326.25

7.25x + 9.50y = 382.50

 

Subtract the first equation from the second.

 

2.25y = 56.25

y = 25 hour

Kyle will work landscaping for 25 hours.