Question

A phone company offers two monthly charge plans. In Plan A, the customer pays a monthly fee of $35 and then an additionat 6 cents per minute of use. In Plan B, the customer pays a monthly fee of $40.20 and then an additional 5 cents per minute of use. For what amounts of monthly phone use will Plan A cost no more than Plan B? Use m for the number of minutes of phone use, and solve your inequality for m.

Answer 1

Plan A will cost no more than Plan B.

Explanation:

Let's set up the inequality to determine the range of monthly phone use (m) for which Plan A costs no more than Plan B.

For Plan A:

Total cost of Plan A = $35 + $0.06m

For Plan B:

Total cost of Plan B = $40.20 + $0.05m

To find the range of monthly phone use where Plan A is cheaper than Plan B, we need to solve the inequality:

$35 + $0.06m ≤ $40.20 + $0.05m

Let's simplify the inequality:

$0.06m - $0.05m ≤ $40.20 - $35

$0.01m ≤ $5.20

Now, divide both sides of the inequality by $0.01 to solve for m:

m ≤ $5.20 / $0.01

m ≤ 520

Therefore, for monthly phone use (m) up to and including 520 minutes, Plan A will cost no more than Plan B.