SOLUTION: To stimulate his son in the pursuit of mathematics a math professor offered to pay is son $8 for every equation correctly solved and to fine him $5 for every incorrect solution. At

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Question 136710: To stimulate his son in the pursuit of mathematics a math professor offered to pay is son $8 for every equation correctly solved and to fine him $5 for every incorrect solution. At the end of 26 problems, neither owed any money to the other. How many did the boy solve correctly?
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Let C = the number of correct solutions and I = the number of incorrect soltion.
1) C%2BI+=+26 The total number of problems is 26.
2) C%288%29+-+I%285%29+=+0 $8 times the number of correct solutions minus $5 times the number of incorrect solutions is zero.
Rewrite equation 1) as:
I+=+26-C and substitute into equation 2):
C%288%29-%2826-C%295+=+0 Simplify and solve for C.
8C-%28130-5C%29+=+0
13C-130+=+0 Add 130 to both sides.
13C+=+130 Divide both sides by 13.
C+=+10 The number of correctly solved problems is 10.
Check:
10%288%29-16%285%29+=+80-80=0