Help Algebra/Word Problems

Question

A phone company offers two monthly plans. Plan A costs $9 plus an additional $0.16 for each minute of calls. Plan B costs $24 plus an additional $0.11 for each minute of calls.

For what amount of calling do the two plans cost the same?

What is the cost when the two plans cost the same?

Answer 1

We have two plans, and we can model the price of each plan with an equation.

1. Plan A: cost = 9 + .16m
2. Plan B: cost = 24 + .11m

m is the minutes. The first part asks at how much calling (how many minutes), do the two plans cost the same. We want the costs to be equal, so we say that the costs are equal. And when we have two equations both with the same variable, we can substitute the variables for each other. So set the costs equal

1. 9 + .16m = 24 + .11m
2. Solve for m
3. .16m - .11m = 24-9
4. .05m = 15
5. m = 300

At 300 minutes, the costs will be equal.

For the second part, what is the cost when the two plans are equal. We know this happens at 300 minutes, so we plug this into either equation. Either because both would be equal at that point. I randomly chose plan A

1. cost = 9 + .16(300)
2. cost = 9+48
3. cost = 57

At 300 minutes, both plans will cost $57

Extra: If you like to think visually, you can imagine the equation to both plans as a line. The point where they are equal minutes and costs is the point the lines intersect. That is why we can substitute the costs for the first part. Its just putting two equations equal to each other to find the point of intersection.