A certain telephone company offers two plans, A and B. Under plan A, the company charges a total of $0.60 for the first 7 minutes of each call and $0.06 per minute thereafter. Under plan B, the company charges $0.08 per minute of each call. What is the duration of a call, in minutes, for which the company charges the same amount under plan A and under plan B?
A. 2
B. 9
C. 15
D. 21
E. 30
Under plan A, the cost of the first 7 minutes = 60 cents.
Since plan B charges 8 cents per minute, the cost of the first 7 minutes under plan B = 7*8 = 56 cents.
Plan B needs to catch up by 4 cents.
We can plug in the answers, which represent the total time required for the two plans to charge the same amount.
After the first 7 minutes, the difference between plan B's rate and plan A's rate = 8-6 = 2 cents per minute.
Since plan B is behind plan A by only 4 cents, it will not take long for plan B to catch up to plan B.
Thus, answer choice B -- which implies that only 2 additional minutes are needed -- seems almost certain to be correct.
Answer choice B: 7 minutes + 2 additional minutes
Total cost for plan A = 60 + 2(6) = 72.
Total cost for plan B = 56 + 2(8) = 72.
Success!
The correct answer is
B.
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