For what amount of calling do the two plans cost the same? and What is the cost when the two plans cost the same?

Question

A phone company offers two monthly plans. Plan A costs $28

 plus an additional $0.13

 for each minute of calls. Plan B costs $16

 plus an additional $0.15

 for each minute of calls.

Answer 1

Define the variables and solve this step by step.

1. Let x be the number of minutes of calls.
2. Plan A: Costs $28 per month plus $0.13 for each minute of calling, so the total cost of Plan A is:
3. Cost of Plan A = 28 + 0.13x
4. Plan B: Costs $16 per month plus $0.15 for each minute of calling, so the total cost of Plan B is:
5. Cost of Plan B = 16 + 0.15x

We need to find when the two plans cost the same, which means setting the cost equations equal to each other:

28 + 0.13x = 16 + 0.15x

12 = 0.02x

x = 600

Now that we know the two plans cost the same when x = 600, we can substitute x = 600 into either cost equation to find the cost:

Cost of Plan A = 28 + 0.13(600) = 106

Therefore, the two plans cost the same at 600 minutes, and the cost when they are the same is $106.

Hope this was helpful.

Answer 2

a = 28 + 0.13 m

b = 16 + 0.15 m

Set the equations equal to each other:

28 + 0.13 m = 16 + 0.15 m

12 = 0.02 m

m = 12 / 0.02 = 600

The cost for 600 minutes is $106.00 (either plan).

The plans cost the same when 600 minutes (10 hours) of time has been used.