AlgebraEasy–MediumSolve a system arising from a training plan
Algebra practice question
A marathon training plan for one week includes only short runs of 4 miles each and long runs of 10 miles each. That week the plan calls for a total of 9 runs covering a total of 54 miles.
How many long runs does the plan call for that week?
Answer: 3
Let s be the number of short runs and L the number of long runs. Then s + L = 9 and 4s + 10L = 54. Substituting s = 9 - L gives 4(9 - L) + 10L = 54, so 36 + 6L = 54, 6L = 18, and L = 3 (with s = 6; check: 4(6) + 10(3) = 24 + 30 = 54). A student who answers 6 has found the number of short runs instead of long runs; a student who answers 5.4 has divided 54 by 10 and ignored the short runs.
Common wrong answers
- If you answered 6
- That's s, the number of short runs. The question asks for long runs: L = 9 - 6 = 3.
- If you answered 9
- That's the total number of runs, not just the long ones; solving 4(9 - L) + 10L = 54 gives L = 3.
- If you answered 5.4
- You divided 54 by 10 and ignored the 4-mile short runs; use s + L = 9 with 4s + 10L = 54 to get L = 3.
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