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
[tex]y=150+30x[/tex] ...(i)
Cost equation for Evelyn's cell phone is
[tex]y=450+20x[/tex] ...(ii)
Equate (i) and (ii) to find the time after which the costs for the girls’ cell phone plans the same.
[tex]150+30x=450+20x[/tex]
[tex]30x-20x=450-150[/tex]
[tex]10x=300[/tex]
Divide both sides by 10.
[tex]x=\dfrac{300}{10}[/tex]
[tex]x=30[/tex]
Therefore, the costs for the girls’ cell phone plans the same after 10 months.
