AlgebraVery hardComparing two linear models
Algebra practice question
Two internet plans charge a fixed monthly fee plus a rate for each gigabyte of data used. For m gigabytes, plan A costs 30 + 0.20m dollars and plan B costs 54 + 0.08m dollars.
For what number of gigabytes do the two plans cost the same amount?
- A. 120
- B. 200Correct
- C. 300
- D. 700
Answer: B. 200
Set the two costs equal: 30 + 0.20m = 54 + 0.08m. Collect the m terms on one side and the constants on the other: 0.20m - 0.08m = 54 - 30, so 0.12m = 24 and m = 200. (Check: plan A costs 30 + 40 = 70; plan B costs 54 + 16 = 70.)
Why the other answers are wrong
- A. 120
- You divided the fee difference by plan A's rate alone: 24 / 0.20 = 120. Both plans charge per gigabyte, so use the DIFFERENCE of the rates, 0.12.
- C. 300
- You divided the fee difference by plan B's rate alone: 24 / 0.08 = 300. The rates must be combined into a difference first.
- D. 700
- You added the fixed fees instead of subtracting them: 84 / 0.12 = 700. The plans cost the same when the difference in fees is cancelled by the difference in rates.
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