A person is choosing between two cell phone plans. Data Plan A has a monthly fee of $46 and a charges $11 per gigabyte(GB). Data Plan B has a monthly fee of $41 and charges $16 per GB.

Question

Define the variables, write a system of linear equations that describes the situation, determine how many GB of data will the costs of the two plans be the same, and what the cost of the plans is, and if the person uses 8gb of data per month, which plan is a better deal and by how much?

Answer 1

Plan A: C = 46 +11G

Plan B: C = 41 +16G

set them equal and solve for G

46 + 11G = 41 + 16G

16G-11G = 46-41

5G = 5

G = 5/5 = 1

C= 46 +11(1) = 46+11 = $57 per month for either plan if just 1 GB

for 8GB

Plan A costs 46+11(8) = 46+88 = $134

Plan B costs 41 + 16(8) = 41+128 = $169

Plan A is less expensive if you use 8 GB per month

you save 169-134 = $35 by using A instead of B