SOLUTION: to stimulate his daughter in the pursuit of problem solving, a math professor offered to pay her $8 for every equation correctly solved and to fine her $5 for every incorrect solut

Question 15167: to stimulate his daughter in the pursuit of problem solving, a math professor offered to pay her $8 for every equation correctly solved and to fine her $5 for every incorrect solution. At the end of the first 26 problems of this problem set, neither owed any money to the other. How many problems did the daughter solve?
I found out the answer is ten I don't know how to set this problem up to get the answer 10.
Answer by rapaljer(4671) (Show Source): You can put this solution on YOUR website!
If there are 26 problems, let x = number right, and therefore the number wrong will be all the rest, which is 26-x. The equation is due to the fact that 8 times the number right minus 5 times the number wrong equals zero.

8x - 5(26-x) = 0
8x - 130 + 5x = 0
13x - 130=0
13x -130 + 130 = 0+130
13x = 130
x= 10 Questions right
26-10 = 16 Questions wrong

Check: $8*10 - $5*16 = 0

R^2 at SCC
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