Question 176076: Jasmine is deciding between two cell-phone plans. The first plan has a $50 sign-up fee and costs $20 per month. The second plan has a $30 sign-up fee and costs $25 per month. After how many months will the total costs be the same? What will the be? If Jasmine has to dign a one-year contract, which plan will be cheaper?
Answer by EMStelley(208)   (Show Source):
You can put this solution on YOUR website! First we need a variable to keep track of the number of months, let's call that m. Then for the first plan (50 for sign up and 20/month), the cost would be:
Cost = 50+20m
For the second plan (30 for sign up and 25/month), the cost would be:
Cost = 30+25m
To find out when they are the same, we just set them equal to each other:
50+20m = 30+25m
Subtract 20m from both sides:
50=30+5m
Subtract 30 from both sides:
20=5m
Divide both sides by 5:
4=m
So the plans will cost the same after 4 months. To know what that cost is, we just plug m=4 into either equation:
Cost = 50+20(4)=50+80=$130
To find out the cost of each after a year (12 months), we plug in m=12 into both.
50+20(12)=$290
30+25(12)=$330
So the first plan is cheaper for a one-year contract.
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