Question

A phone company offers two monthly plans. Plan A costs $25 plus an additional $0.07 for each minute of calls. Plan B costs $16 plus an additional $0.09 for each minute of calls. Q1: For what amount of calling do the two plans cost the same? Q2: What is the cost when the two plans cost the same?

Answer 1

Answer:

1) For 450 minutes of calling the two plans cost the same.

2) The cost when the two plans cost the same is $56.5.

Step-by-step explanation:

The cost of both plans can be modeled by linear functions.

Plan A:

$25 plus an additional $0.07 for each minute of calls.

So, for t minutes of calls, the cost is:

$A(t) = 25 + 0.07t$

Plan B:

$16 plus an additional $0.09 for each minute of calls.

So, for t minutes of calls, the cost is:

$B(t) = 16 + 0.09t$

Q1: For what amount of calling do the two plans cost the same?

This is t for which:

$A(t) = B(t)$

$25 + 0.07t = 16 + 0.09t$

$0.02t = 9$

$t = \frac{9}{0.02}$

$t = 450$

For 450 minutes of calling the two plans cost the same.

Q2: What is the cost when the two plans cost the same?

This is A(450) or B(450), since they are the same.

$B(450) = 16 + 0.09*450 = 56.5$

The cost when the two plans cost the same is $56.5.