phone service and inequality

by wc

For his phone service, Ryan pays a monthly fee of $13.00, and he pays an additional $0.05 per minute of use. The least he has been charged in a month is $72.45.

What are the possible numbers of minutes he has used his phone in a month?

Use m for the number of minutes, and solve your inequality for m.


Let m be the number of minutes used.

Monthly cost = fixed cost + variable cost

fixed cost = 13

Variable cost = 0.05 × m

Monthly cost = 13 + 0.05m

It says in the problem that the least he has been charged in a month is $72.45.

This means that the monthly cost is at least 72.45.

In other words, the monthly cost is 72.45 or bigger.

This can be expressed as 13 + 0.05m ≥ 72.45

Just solve the inequality.

13 + 0.05m ≥ 72.45

13 - 13 + 0.05m ≥ 72.45 - 13

0 + 0.05m ≥ 72.45 - 13

0.05m ≥ 59.45

Divide both sides by 0.05

0.05m/ 0.05 ≥ 59.45/0.05

m ≥ 1189

Ryan used at least 1189 minutes

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