SOLUTION: In order to encourage his son to study arithmetic, a father agrees to pay his boy $8 for every problem correctly solved and to fine him $5 for each incorrect solution. At the end

Question 553034: In order to encourage his son to study arithmetic, a father agrees to pay his boy $8 for every problem correctly solved and to fine him $5 for each incorrect solution. At the end of 26 problems, neither owes anything to the other. How many problems did the boy solve correctly
Answer by htmentor(1343) (Show Source): You can put this solution on YOUR website!
In order to encourage his son to study arithmetic, a father agrees to pay his boy $8 for every problem correctly solved and to fine him $5 for each incorrect solution. At the end of 26 problems, neither owes anything to the other. How many problems did the boy solve correctly
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Let c = the number of correct problems
Let w = the number of wrong problems
At the end of 26 problems, the boy does not owe anything:
8c - 5w = 0
And since the total number is 26, the sum of the correct and incorrect problems totals 26:
c + w = 26
Solve for w in the 2nd equation and substitute in the 1st:
8c - 5(26-c) = 0
13c = 130
c = 10
So the boy solved 10 problems correctly
Check:
10*8 - 16*5 = 0 = 80 - 80
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