A phone company plan

Question

A phone company has two long distance calling plans. The first plan is $25 per month for unlimited calling. The second plan is $10 per month plus $0.05 per minute of long distance calling. After how many minutes of long distance calls will it be cheaper for a costumer to purchase the first plan?

Answer 1

You can start by writing out what is given in a rough conceptual way:

For one company the monthly bill = 25 dollars per month

For another company the monthly bill = 10 dollars per month + 0.05 (minutes of long distance calling)

We can see that we have two linear relationships, where the minutes of long distance calling are the independent variable and the overall monthly bill is the dependent variable:

y = 25 + 0x = 25

y = 10 + 0.05x

The point at which these two lines intersect is the point beyond which the second company's bill will be larger. Graphs intersect when their points are equal (when both their x and y values are the same). Thus we can set y from the first equation equal to the y in the second equation.

25 = y = 10 + 0.05x

25 = 10 + 0.05x

15 = 0.05x

x = 15/.05 = 15/(1/20) = 15*20

x = 300 minutes long distance

After 300 minutes of long distance calling, it will be cheaper for the costumer to purchase the first plan.

Answer 2

You can represent the cost of $10 a month and .05 cent/minute with a linear equation:

the total cost of the plan = 10 +.05m

(where m is number of minutes.)

If the $10 initial fee plan is more expensive (making the unlimited plan cheaper) it will cost more than $25 a month. So after how many minutes will the cost be at or above $25?

Set the expression 10+.05m equal to 25 to find out.

10+.05m=25

-10 -10

Solve for m by subtracting 10 to undo adding 10

.05m=15

÷.05 ÷.05

Solve for m: undo multiplying by .05 by doing the opposite: dividing by .05

m=300

So if you talk exactly 300 minutes the phone programs cost the same amount. Which means any amount over 300 minutes would make the unlimited plan cheaper, because the $10 starting fee plan would cost more than $25 after 300 minutes.