Question

A phone company offers two monthly plans. Plan A costs $19plus an additional $0.11 for each minute of calls. Plan B costs $14plus an additional $0.15for each minute of calls. For what amount of calling do the plans cost the same? What is the cost when the two plans cost the same?

Answer 1

Let x be the number of minutes and y be the total cost. Then, for plan A we have

`y=0.11x+19`

and for plan B, we have

`y=0.15x+14`

In order to find the number of minutes where the plans cost the same, we need to find the intersection point of the two equations. Then, we need to solve the following system of equations:

`\begin{gathered} y=0.11x+19 \\ y=0.15x+14 \end{gathered}`

Then, by substituting equation 2 into 1, we get

`0.15x+14=0.11x+19`

By subtracting 0.11x and 14 to both sides, we have

`0.04x=5`

Then, x is given by

`\begin{gathered} x=(5)/(0.04)=125 \\ \end{gathered}`

For what amount of calling do the plans cost the same? For one minute of calls, the plans cost the same at 125 calls.

Now, in order to find the cost, we need to substitute the last result into one of our 2 equations. If we substitute x=125 into equation 1, we have

`y=0.11(125)+19`

which gives

`\begin{gathered} y=0.11(125)+19 \\ y=32.75 \end{gathered}`

What is the cost when the two plans cost the same? The answer is $32.75