In order to encourage his son to study maths, a father agrees to pay his boy 8 cents for each problem correctly solved and to fine him 5 cents 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
Ten problems
Let x represent the number of problems answered correctly, then 26-x represents the number of problems answered incorrectly:
8x – 5(26-x) = 0
8x – 130+5x = 0
13x = 130
x = 10
26-x = 16
Therefore, 10 answers were correct and 16 were incorrect.