Question

One prepaid cell phone company charges $0.029 per minute and a $2 monthly fee. Another company charges $0.033 per minute with no monthly fee. For what number of minutes per month are the charges for the first company cheaper?

Answer 1

For more than 500 minutes

Explanation:

Let x be the number of minutes.

First company charges:

$0.029 per minute, then $0.029x for x minutes

and a $2 monthly fee.

In total, $(0.029x+2)

Second company charges:

$0.033 per minute, then $0.033x for x minutes

with no monthly fee.

If the charges for the first company are cheaper, then

`0.029x+2<0.033x`

Multiply this inequality by 1,000:

`29x+2,000<33x\\ \\33x-29x>2,000\\ \\4x>2,000\\ \\x>500`