Question

For what numbers of minutes of local cost are the cost of the plans the same?

Answer 1

b. 75 minutes

EXPLANATION :

We can formulate a relation with the cost and minutes :

`y=mx+b`

where y = total cost

x = number of minutes

m = cost per minute of calls

and

b = fixed monthly fee

The first company charges b = $27.95 monthly fee and the rate is m = $0.12 per minute

The equation will be :

`y=0.12x+27.95`

The next company charges b = $12.95 a month and the rate is m = $0.32 per minute.

The equation will be :

`y=0.32x+12.95`

We are looking for the number of minutes (x) in which the total cost (y) are the same for both companies.

So we can equate y = y

`\begin{gathered} y=y \\ 0.12x+27.95=0.32x+12.95 \end{gathered}`

Solve for x :

`\begin{gathered} 0.12x-0.32x=12.95-27.95 \\ -0.2x=-15 \\ x=(-15)/(-0.2) \\ \\ x=75 \end{gathered}`