creating a system of equation

Question

Daniel is choosing between two cellphone plans. "Plan A" charges $80 per month, which includes unlimited text messaging. "Plan B" cost $20 per month plus $0.15 per text message. What is the system of equation that represents the fees of both "Plan A" and "Plan B".

Answer 1

Plan A is simply a constant cost function of A(x) = 80 where x is the # of text messages

Plan B is a linear cost function B(x) = 0.15x + 20

80 = 20 + 0.15x

60 = 0.15x

6000 = 15x

x=400

you can send 400 text messages under plan B for the prices to be the same

So x<400 text messages, then plan B is the better buy. Otherwise plan A