math question need help

Question

A phone company offers two monthly plans. Plan A costs $27 plus an additional %0.12 for each minute of calls. Plan B costs $20 plus an additional $0.14 for each minute of calls. For what amount of calling do the two plans cost the same?

Answer 1

For this kind of problem, we can write an equation of a line that represents each of these phone plans.

Plan A: $27 plus $0.12 per minute

Plan B: $20 plus $0.14 per minute

If we let "x" represent the number of minutes on a call, and let "y" represent the total cost, then we can write the following two equations.

Plan A: y = 0.12x + 27

Plan B: y = 0.14x + 20

You could plot each of these lines using a graphing program, and find the point at which they intersect. The x-coordinate of the intersection point will be the number of minutes at which the cost of each plan will be the same.

Another way to find this value of "x" is to set the two equations equal to one another, and then solve for "x".

0.12x + 27 = 0.14x + 20

27 = 0.02x + 20 [subtract 0.12x from both sides]

7 = 0.02x [subtract 20 from both sides]

350 = x [divide by 0.02 on both sides]

Therefore, the number of minutes at which the two phone plans cost the same amount is 350 minutes.