How many minutes would you have to use in a month in order for the second plan to be preferable?

Question

You are choosing between two different cell phone plans. The first plan charges a rate of 26 cents per minute. The second plan charges a monthly fee of $29.95 plus 11 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

How many minutes would you have to use in a month in order for the second plan to be preferable?

You are choosing between two different cell phone plans. The first plan charges a rate of 26 cents per minute. The second plan charges a monthly fee of $29.95 plus 11 cents per minute.

How many minutes would you have to use in a month in order for the second plan to be preferable?

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When you evaluate word problems ALWAYS look for the equations hidden within the words and the unknown values that you are trying to find.

Plan 1 .... .Let T1 and T2 be the total cost for 1 month so.....for Plan 1 T1= 26x

Plan 2 .... T2 = 29.95 + .11x

now when T1 = T2 the totals are the same. We want number of minutes when T2 < T1....so....

.26x = 29.95 + .11x ....now we find x when the plan minutes are equal....

.15x = 29.95

x = 29.95/.15 = 199.6666 ..... when x = 199 minutes amounts are equal .....check....

Plan 1...... (.26)199 = 51.74...... (.26)200 = 52

Plan 2 .... 29.95 + (.11)199 = 29.95 + 21.89 =51.84......(.11)200 + 29.95 = 51.95

----What is being asked-----

How many minutes would you have to use in a month in order for the second plan to be preferable?

Notice at 199 minutes plan 1 is still preferable because $51.74<$51.84.....but at....

........at 200 minutes plan 2 is preferable because $51.95 < $52........right? So 200 minutes is the number right?

Answer 2

Plan 1 cost = 0.26m

Plan 2 cost = 29.95 + 0.11m

with m = minutes

Set P1 = P2 to find intersection of 2 functions (= equal cost under both plans)

0.26m = 29.95 + 0.11m

=> 0.26m - 0.11m = 29.95

=> m = 29.95 / 0.15

=> 199 2/3 minutes

for 200 minutes or more, plan 2 is cheaper.