The company charges a monthly service fee of $20 for either plan the customer chooses:

Question

Talk and Text Plan A charges five cents a minutes and twenty dollars for 250 texts. Talk and Text Plan B charges ten cents a minute (first 100 minutes free) and fifteen dollars for 200 texts. Which plan is better based on the number of text messages you send per month if you only have $75 to spend each month.

What are the system of equations for this problem? 

Answer 1

You want to set up a system of equations with two variables. So set T as the number of texts and M to minutes used.

With this in mind you can make a system of equations for the two plans:

Plan A is 0.05M + 0.08T = 75 (calculating the rate of price per text and setting it equal to your money).

Plan B is 0.1(M - 100) + 0.075T = 75 but you want to collect like terms so 0.1M + 0.075T = 85 is the resulting calculation (in this case, we also calculate price per text and set it equal to your 75 dollars).

So the basic answer is... Plan B will always be better for you will texting, because it is cheaper for texting always, BUT if want to know at what amount of texts and minutes used that these plans are equal at a rate of $75 dollars than you would solve the system of equations.

The two plans are the same at approximately 765 texts and 276 minutes when spending $75 a month.

There is possibility a discrepancy in the question as to what the required answer is.