AlgebraHardInequality from a rate comparison
Algebra practice question
Plan A charges $0.10 per text message with no monthly fee. Plan B charges a $6 monthly fee plus $0.04 per text. For how many texts t per month is Plan B cheaper than Plan A?
- A. t > 100Correct
- B. t < 100
- C. t > 60
- D. t > 150
Answer: A. t > 100
B cheaper: 6 + 0.04t < 0.10t, so 6 < 0.06t and t > 100.
Why the other answers are wrong
- B. t < 100
- For t < 100, Plan A is cheaper.
- C. t > 60
- 60 is 6/0.10, comparing the fee to A's rate alone.
- D. t > 150
- 150 is 6/0.04, comparing the fee to B's rate alone.
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