How many GB of usage would result in both plans costing the same amount for that month?

Question

A phone service provider offers two data plans. Plan A costs $10 per month plus $5 for each gigabyte (GB) used during that month. Plan B costs $20 per month plus $3 per GB used during that month.

Answer 1

This is the very typical break-even calculation.  Set the 2 equations equal to each other:

 

EQ 1:  TC=10+5x

EQ 2:  TC=20+3x

 

       So, 10+5x=20+3x

            -10 -3x  -10  -3x

 

              2x = 10

 

                     Divide out both sides by 2, to get:x=5

 

               So, at exactly 5GB of data, the 2 plans cost the same