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Dr. Johnson promises to pay his son $5.00 for each correct answer he obtains in his math homework.
For each incorrect answer, the son must pay his father $8.00.
The boy answered twenty-six math questions.
At the end, no money was exchanged.

How many correct and incorrect answers did the boy get?

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Answer: 

Let C be the number of correct questions and I be the number of incorrect questions. Then, since no money was exchanged, 5C=8I. Also, C+I=26. Hence, C=26-I, and, therefore, 5(26-I) = 8I. Opening parentheses, we get 130 – 5I = 8I, or 13I=13.  Therefore, I=10, and C=16. So the boy got 16 correct and 10 incorrect answers.

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