Question

Anna’s cell phone plan charges her $30 per month plus a $150 one-time activation fee. Evelyn’s cell phone plan charges her $20 per month, plus a $450 one-time activation fee. After how many months are the costs for the girls’ cell phone plans the same?

Answer 1

Given:

Anna’s cell phone plan charges her $30 per month plus a $150 one-time activation fee.

Evelyn’s cell phone plan charges her $20 per month, plus a $450 one-time activation fee.

To find:

The number of months after which the costs for the girls’ cell phone plans the same.

Solution:

Let x be the number of months.

Total cost = Fixed cost + Variable cost

According to the question, cost equation for Anna’s cell phone is

$y=150+30x$           ...(i)

Cost equation for Evelyn's cell phone is

$y=450+20x$         ...(ii)

Equate (i) and (ii) to find the time after which the costs for the girls’ cell phone plans the same.

$150+30x=450+20x$

$30x-20x=450-150$

$10x=300$

Divide both sides by 10.

$x=\dfrac{300}{10}$

$x=30$

Therefore, the costs for the girls’ cell phone plans the same after 10 months.