Question

Your cell phone company offers you a choice between two promotional deals. You can either get 500 free text messages with a charge of $0.10 for each text message over 500, or you can get 400 free text messages with a charge of $0.20 for each text message over 400. How many text messages would you have to send for the cost to be the same for either plan? 

Answer 1

Call the plans A and B. Call the number of texts T.

A=0.10(T-500) and B=0.20(T-400). If A=B, 0.10T-50=0.20T-80.

30=0.10T, T=300, but this is less than the number required for free texts. A and B=-20. 

The standard charge is required to make comparisons.

If a is the standard charge for A and b for B,

30+a-b=0.10T and T=10(30+a-b). The difference in the standard fixed charges impacts on T.

This means that T>500, 10(30+a-b)>500, 30+a-b>50, a-b>20. For example if a-b=50, T=800.