Math CentralQuandaries & Queries


Question from Confused, a parent:

Justin and his father went fishing and together caught 12 fish. Three times the number of fish that Justin caught exceeds 12 by as much as 5 times the number that his father caught exceeds 8. How many fish did each catch?


No one but mathematics textbook authors use such bizarre wordings. It always seems to me that the intent is to obfuscate the problem rather than illuminate it.

Suppose Justin caught $J$ fish and his father caught $F$ fish. "Three times the number of fish that Justin caught" is then $3 \times J.$ This number exceeds 12 and hence it is more than 12 and the amount by which it exceeds 12 is $3 \times J - 12.$

"5 times the number that his father caught" is $5 \times F$ and the amount that this exceeds 8 is $5 \times F - 8.$

These two quantities are equal and hence

\[3 \times J - 12 = 5 \times F - 8.\]

Together they caught 12 fish so that gives you a second equation

\[J + F = 12.\]

Solve these two equations for $J$ and $F.$

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