Finding a variable

[Shoppingal]

A company recieved a bill from its accountant for $3310, representing a combined total of 41 "billable" hours both the CGA and his accounting assisant, for couducting the company's audit. If the CGA charges her time at $120 per hour and the assisant's time at $50 per hour, how many hours did the CGA work on the audit?

Let x represent the CGA's rate x=120

Let y represent the assistants rate y=50

Total hours = 41

Total cost $3310

120x + 50y = 3310
120x + 50y = 3310

-70x = 162190

The answer is 18 but everything I try is just not getting me there. Thanks for any help that is provided.

 

[rbcc]

Hi,

so you set up one equation correctly 120x+50y=3310 but you have 2 unknowns so you need another equation before you can solve for both variables. so 41=x+y would be the other one that you need that comes from the number of hours each of them worked. Another thing is that from your first equation 120x+50y=3310 the x and y represent the number of hours worked, not the pay they recieved.

now just use substitution to solve

41-y=x
120x+50y=3310
120(41-y)+50y=3310
4920-120y+50y=3310
4920-3310=70y
23=y
x=41-23=18

Hope that helps!

 

[Shoppingal]

Thank you so much, I'm just going back too school after many years and this stuff is so confusing. I appreciate the help.