Your cell phone plan costs ​$24.99 per month plus ​$0.18 for each text message you send or receive. You have at most ​$30 to spend on your cell phone bill.

Question

Your cell phone plan costs

​$24.9924.99

per month plus

​$0.180.18

for each text message you send or receive. You have at most

​$3030

to spend on your cell phone bill. What is the maximum number of text messages that you can send or receive next​ month?

Answer 1

You can do this one of two ways:

Way 1-algebraically

You can set up an equation and solve. Our total cost consists of the $24.99 plan payment plus an additional $0.18 for every text sent/received.

Let the number of texts we can send and receive be denoted by x.

Thus the cost is 24.99+0.18x.

We have a total of $30 to spend monthly, so we can set up the equation 30=24.99+0.18x.

Solving for x we get 27.833 but we need to take 27 so that we don't exceed the $30 budget (sending/receiving the 28th text would put us over 30 by 3 cents)

So x=27

Or way 2- graphically

We have our cost function defined by y=0.18x+24.99

We can make a second equation of y=30 as our budget

Graphing both of those we get that once again x=27.833 is their intersection

By the same logic as before we will take x=27

Hope this helps!