Judy worked 8 hours and ben worked 10 hours. their combined pay was $80. when judy worked 9 hours and ben worked 5 hours. their combined pay was $65. find the hourly rate for each person

Define x and y:

Let Judy's hourly rate be x.
Let Ben's hourly rate be y.


Construct Equation:

8x + 10y = 80 (1)
9x + 5y = 65  (2)


From Equation (1):

8x + 10y = 80 
4x + 5y = 40          // Divide by 2


Equation (2) - (1):

5x = 25
x  = 5                 //Divide by 5


Substitute x = 5 into Equation (1):

4x + 5y = 40
4(5) + 5y = 40    //Sub x = 5
20 + 5y = 40 .    //Simplify
5y = 40 - 20       //Subtract 20 from both sides
5y = 20              //Simplfy
y = 4                  // Divide by 4


Find Judy's and Ben's Rate:

Judy = x = $5/hr
Ben = y = $4/hr


Ans: Judy's hourly rate is $5 and Ben's hourly rate is $4.