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.