You to choose from a cellphone company that offers 2 plans. The company charges a monthly service fee of 20 dollars for either plan the costumer chooses

Question

plan A- charges 5 cents a minute and 20 dollars for 250 texts. 

Plan B- charges 10 cents a minute, first 100 minutes free, and 15 dollars for 200 tex.

you only have 75 dollars to spend each month

Answer 1

Hi Emily,

 

You've started this problem off well and just need to write your 2 equations by translating the words into symbols in order to finish it. Since both start with a monthly service fee of $20, it will need to be included in both equations as a starting point. You also need to identify your variable. Although it seems as though there should be 2 variables, there is actually only 1 because there is a set rate for the texts and neither plan takes into account exceeding the text limit. Therefore, the variable you will define and solve for will be the number of minutes.

 

Let's say that m=minutes. Plan A is straight forward and the expression is $0.05m+$20 service fee + $20 for the 250 texts. Assuming that you don't go over 250 texts, the simplified expression is now $0.05m+$40.

 

For Plan B, we'll do something similar for its expression. The only difference is that the first 100 minutes are free. This means that the per minute charge is actually going to be for m-100 because we have to subtract 100 minutes. We also have to assume that you will use at least 100 minutes since there is no money being given back and we must assume that you will not go over 200 texts. Now, our Plan B expression looks is $0.10(m-100)+$20 service fee+$15 for the 200 texts. Once again we simplify assuming that you don't go over the 200 texts and our expression is now $0.10(m-100)+$35.

 

You now have 2 expressions and are able to determine which plan is better for the $75 being spent each month by setting each expression equal to $75 and solving for your variable.