Which inequality represents the possible numbers n of layers the scientist can analyze in the available laboratory time?

Question

A climate scientist is measuring the chemical composition of layers in an ice core. Setting up her equipment takes 90 minutes, and each layer she analyzes after that takes 15 minutes. She has at most 480 minutes of laboratory time available.

Accepted Answer

A. 15n + 90 ≤ 480. Each of the n layers takes 15 minutes, giving 15n minutes, plus the 90-minute setup, for a total of 15n + 90 minutes. Because at most 480 minutes are available, 15n + 90 ≤ 480. Choice B reverses the inequality symbol, treating 'at most' as 'at least.' Choice C subtracts the setup time instead of adding it to the total. Choice D interchanges the rate and the fixed time, multiplying the 90-minute setup by the number of layers.

Answer

B. 15n + 90 ≥ 480 — You set up the times correctly, but 'at most 480 minutes' means the total can't exceed 480, so the symbol must be ≤, not ≥.

Answer

C. 15n − 90 ≤ 480 — The 90-minute setup adds to her total lab time, so it should be 15n + 90, not 15n − 90.

Answer

D. 90n + 15 ≤ 480 — You swapped the two numbers: 15 is the per-layer rate that gets multiplied by n, and 90 is the one-time setup.

Algebra practice question

Answer: A. 15n + 90 ≤ 480

Why the other answers are wrong

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