What is the length, in miles, of the Summit Trail?

Question

The Highland Preserve trail network has exactly three trails: the Meadow Trail, the Summit Trail, and the Ravine Trail. The Summit Trail is 4 miles shorter than twice the length of the Meadow Trail, and the Ravine Trail is 3 miles longer than the Meadow Trail. The three trails have a combined length of 43 miles.

Accepted Answer

C. 18. Let m be the length of the Meadow Trail. Then the Summit Trail is 2m - 4 and the Ravine Trail is m + 3, so m + (2m - 4) + (m + 3) = 43, which gives 4m - 1 = 43, so 4m = 44 and m = 11. The Summit Trail is 2(11) - 4 = 18 miles. Check: 11 + 18 + 14 = 43. Choice A is the Meadow Trail length (stopping after solving for m instead of answering the question asked). Choice B is the Ravine Trail length (answering for the wrong trail). Choice D is 2m = 22, the result of dropping the '- 4' when evaluating the Summit Trail expression.

Answer

A. 11 — That's m, the Meadow Trail length. You solved the equation correctly but stopped there — plug it into 2m - 4 to get the Summit Trail.

Answer

B. 14 — That's the Ravine Trail (m + 3 = 14). The question asks for the Summit Trail, 2m - 4.

Answer

D. 22 — You found m = 11 and doubled it but dropped the '- 4': the Summit Trail is 2(11) - 4 = 18.

Algebra practice question

Answer: C. 18

Why the other answers are wrong

More Algebra questions