Question

7) Solve the problem: When making a long

distance call from a certain pay phone, the
first three minutes of a call cost $2.00. After
that, each additional minute or portion of a
minute of that call costs $0.50.0 Use an
inequality to find the maximum number of
minutes one can call long distance for
$10.00

Answer 1

19 minutes

Explanation:

Let x be the number of minutes the call lasts.

The first three minutes of a call cost $2.00.

Then
`x-3` minutes left.

Each additional minute or portion of a minute of that call costs $0.50, so
`x-3` minutes cost
`\$0.50(x-3).`

The total cost is

`\$2+\$0.50(x-3)`

The price of the call is $10.00, so the maximum number of minutes one can call long distance for $10.00 can be calculated from the inequality

`2+0.50(x-3)\le 10\\ \\20+5(x-3)\le 100\ [\text{Multiplied by 10}]\\ \\20+5x-15\le 100\\ \\5x+5\le 100\\ \\5x\le 100-5\\ \\5x\le 95\\ \\x\le 19`

When x=19, the cost of the call is $10.00. When x<19, then the price of the call is less than $10.00.