phone service and inequality

by wc
(gresham)

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.

Solution


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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