#### 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.