Question

You have two jobs. One job pays nine dollars per hour and the other job pays $7.50 per hour. You worked 18 hours last week and earned $145.50. How many hours did you work at each job?

Answer 1

`Y =(16.5)/(1.5)= 11`

`X = 18-11=7`

And then we conclude that for the first job he works 7 hours and for the second job 11 hours

Explanation:

We can define the following notation:

`X` represent the number of hours worked for one job

`Y` represent the number of hours worked for the other job

`p_x = 9` represent the hourly payment for the first job

`p_y = 7.50` represent the hourly payment for the other job

And we can define the following equations:

`X+ Y= 18` (1) represent the toal number of hours worked

`9X +7.5 Y = 145.50` (2) represent the total amount earned

From equation (1) if we solve for X we got:

`X = 18-Y` (3)

Replacing equation (3) into equation (2) we got:

`9(18-Y) +7.5 Y =145.50`

And after solve the equation we can find the value of Y:

`162 -9Y +7.5 Y =145.50`

`16.5 = 1.5 Y`

`Y =(16.5)/(1.5)= 11`

And solving for X from equation (3) we got:

`X = 18-11=7`

And then we conclude that for the first job he works 7 hours and for the second job 11 hours