Answer
a. 15 months
b. Rocco's
Work Step by Step
For part a, we want to know after how many months the cost would be equal. Alpine's cost is 25 per month plus a 125 sign up fee. Rocco's cost is 30 per month plus a 50 sign up fee. If we set these equal to each other, we get:
$25m+125=30m+50$, $m=$number of months
Subtract $25m$ and $50$ from both sides.
$75=5m$
Divide both sides by $5$.
$15=m$.
The price will be equal after 15 months.
For part b, we want to know which would be cheaper after 12 months. We can solve each equation, substituting 12 for $m$.
$25(12)+125=A$
$A=425$
$30(12)+50=R$
$R=410$
Alpine costs 425 after 12 months, while Rocco's only costs 410. Rocco's is cheaper.