You are choosing between two different cell phone plan

Question

You are choosing between two different cell phone plans. The first plan charges a rate of 21 cents per minute. The second plan charges a monthly fee of $39.95 plus 8 cents per minute. How many minutes would you have to use in a month in order for the second plan to be preferable? 

Answer 1

Let M = the number of MINUTES used in one month

.21M = the total monthly bill for 1st PLAN

.08M + $39.95 = the total monthly bill for the 2nd PLAN

WHEN IS THE 2nd PLAN BETTER THAN THE 1st PLAN?

.21M > .08M + 39.95

21M > 8M + 3995 (Multiply both sides by 100 to remove decimals.)

21M - 8M > 3995 (Subtract 8M from both sides.)

13M > 3995 (Combining like terms.)

13M/13 > 3995/13 (Divide both sides by 13.)

M > 3995/13 (The 13's cancel each other out.)

M > 307.3 MINUTES

Any time more than 307.3 minutes, the 2nd PLAN is less expensive than the 1st PLAN.

CHECKING:

1st PLAN: 307.3 min X $0.21 = $64.53

2nd PLAN: (307.3 min X $0.08) + $39.95 = $24.58 + $39.95 = $64.53

So, at 307.3 minutes the plans have the same amount due.

However, any time after that, the rate of $0.08 cents a minute is lower

than the rate of $0.21 cents a minute.

Hope this helps you Chanelle.