Question

A phone company offers two monthly charge plans. In Plan A, there is no monthly fee, but the customer pays 9 cents per minute of use. In Plan B, the customer pays a monthly fee of 56.60 and then an additional 7 cents per minute of use.

For what amounts of monthly phone use will Plan A cost more than Plan B? Use m for the number of minutes of phone use in a month, and solve your inequality for m.

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Answer 1

Answer: 0.09m > 56.60 + 0.07m, where m > 2830.

Explanation:

Let's assume that Plan A costs more than Plan B for monthly phone use greater than some value m, where m is the number of minutes of phone use in a month.

For Plan A, the monthly cost can be expressed as:

Cost_A = 0 + 0.09m = 0.09m

For Plan B, the monthly cost can be expressed as:

Cost_B = 56.60 + 0.07m

To find the value of m for which Plan A costs more than Plan B, we need to set the two costs equal to each other and solve for m:

0.09m = 56.60 + 0.07m

0.02m = 56.60

m = 56.60 / 0.02

m = 2830

Therefore, for monthly phone use greater than 2830 minutes, Plan A will cost more than Plan B.

In mathematical notation, we can express this as:

0.09m > 56.60 + 0.07m, where m > 2830.