Word Problem: Math Prof Pays His Son...

[geekily]

"To stimulate his son in the pursuit of mathematics, a math professor offered to pay his son $8 for ever question correctly solved and to fine him $5 for every incorrect solution. At the end of 26 questions, neither owed any money to the other. How many did the boy solve correctly?

I started out thinking 8x - 5y = 0. When I realized that wouldn't work, I tried (8x - 5y) (26) = 0. That becomes 208x - 130y = 0, and if you move y to the other side, 208x = 130y. I didn't come up with anything based on that, either. Can someone please give me a hint? It's the last problem on my homework and it's taunting me.

Thanks for your help!

 

[Denis]

c = correct; then wrong = 26 - c

8c = 5(26 - c)

Now go earn $8 :wink:

 

[soroban]

Hello, geekily!

"To stimulate his son in the pursuit of mathematics, a math professor
offered to pay his son $8 for ever question correctly solved
and to fine him $5 for every incorrect solution.
At the end of 26 questions, neither owed any money to the other.
How many did the boy solve correctly?

I started out thinking: \(\displaystyle 8x\,-\,5y\:=\:0\;\) . . . Right!

You overlooked another equation: \(\displaystyle \,x\,+\,y\:=\:26\)
. . (A total of 26 questions)

Now solve the system of equations . . .

 

[geekily]

Thank you both! I think soroban's answer makes more sense to me because I'm more familiar with the set-up, but I really appreciate both responses.