Break even on cell phone plans

[Ronb107]

Homework Statement

A customer is choosing between two cellular phone plans.
One plan has a monthly fee of $50 for an allowance of
500 minutes per month. If the customer uses more than
500 minutes, the charge is $0.35 per additional minute used.
The other plan has a monthly fee of $75 for an allowance of
1000 minutes per month. If the customer uses more than
1000 minutes, the charge is $0.40 per additional minute. After
how many minutes used are the monthly costs of the plans
equal?

Homework Equations

This is how I set it up...
Plan 1: (<=500 min) x= $50; (>500 min) x= $50 + $0.35m
Plan 2: (<=1000 min) x= $75; (>1000 min) x= $75 + 0.40m

The Attempt at a Solution

The answer is 4000 minutes, but I don't know how to proceed. Any help is appreciated.

 

[Mark44]

Homework Statement

A customer is choosing between two cellular phone plans.
One plan has a monthly fee of $50 for an allowance of
500 minutes per month. If the customer uses more than
500 minutes, the charge is $0.35 per additional minute used.
The other plan has a monthly fee of $75 for an allowance of
1000 minutes per month. If the customer uses more than
1000 minutes, the charge is $0.40 per additional minute. After
how many minutes used are the monthly costs of the plans
equal?

Homework Equations

This is how I set it up...
Plan 1: (<=500 min) x= $50; (>500 min) x= $50 + $0.35m
Plan 2: (<=1000 min) x= $75; (>1000 min) x= $75 + 0.40m

A better choice would be C, for cost, and then either x or m for the number of minutes.

The Attempt at a Solution

The answer is 4000 minutes, but I don't know how to proceed. Any help is appreciated.

For starters, try graphing both cost functions on the same axis system. For plan 1, the graph is a horizontal line 50 units up for m in the interval [0, 500]. Then the graph heads off at a slope of .35.

See if you can figure out what the graph for plan 2 looks like, as well.