Olivia is considering two phone plans. Plan A charges $20 per month, plus $0.05 per minute. Plan B charges $15 per month plus $0.10 per minute. How many minutes can Olivia talk so that both plans will cost the same amount? (Hint: Create an equation for each plan where y is the total cost and x is the minutes and then find the solution to the system of equations.)

Let's start by making one for plan a. We know that there is 20 dollars per month, this is the y intercept. Now, although it says per month which can change by x, the problem is mainly asking for minutes.

Remember, a slope intercept equation is

y=mx+b

M is the slope, and x is multiplied to the slope. The slope for an example can be used for this, adam eats 5 apples per day or x, how many apples can he eat in 5 days? We are wanting to know how many he can eat in 5 days, so we of course would multiply 5 by 5. This is basically a slope equation.

So, for plan a, we have y=0.05x+20 where x is minutes

For plan b, we should get

y=0.10x+15 where x is also minutes. The problem is asking use to find which value that we plug in will make both plan a and b correct. Basically, the value we find is x, so we solve for x by setting the two equations equal.

0.05x+20=.10x+15 Use inverse operations

20=.05x+15

5=.05x

x=10

We know if we plug in 10 for x, both would equal the same or 21 dollars.