Phone service and inequality
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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