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Algebra practice question

A rowing team owns single sculls, which seat 1 rower each, and pairs, which seat 2 rowers each. The team owns 14 boats in all, and when every boat is filled to capacity, exactly 22 rowers are seated.

How many pairs does the team own?

Answer: 8

Let s be the number of single sculls and p the number of pairs: s + p = 14 and s + 2p = 22. Subtracting the first equation from the second gives p = 8 (and s = 6). A student who solves for the wrong variable answers 6, and one who divides the 22 rowers by 2 without using the boat total answers 11.

Common wrong answers

If you answered 6
That's s, the number of single sculls — the question asks for pairs, so finish with p = 22 - 14 = 8.
If you answered 11
You divided the 22 rowers by 2 and ignored the 14-boat total; the single sculls each hold only 1 rower, so you need both equations s + p = 14 and s + 2p = 22.
If you answered 14
That's the total number of boats, not the number of pairs; subtract the boat total from the rower total to get p = 8.

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