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
...(i)
Cost equation for Evelyn's cell phone is
...(ii)
Equate (i) and (ii) to find the time after which the costs for the girls’ cell phone plans the same.
Divide both sides by 10.
Therefore, the costs for the girls’ cell phone plans the same after 10 months.