Question

For her phone service, Martina pays a monthly fee of $25, and she pays an additional $0.07 per minute of use. The least she has been charged in a month is $109.14.
What are the possible numbers of minutes she has used her phone in a month?
Use m for the number of minutes, and solve your inequality for m.

Answer 1

Answer: Anything that is 1202 or larger

In other words, $m \ge 1202$

So we could have m = 1202, or m = 1203, or m = 1204, etc.

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Explanation:

• m = number of minutes used
• 0.07m = amount charged for those minutes used excluding the $25
• 0.07m+25 = total monthly bill now including the extra $25 fee

The monthly bill is at least $109.14, since this is the lowest amount she has been charged.

$\text{monthly bill} \ge 109.14\\\\0.07m+25 \ge 109.14\\\\0.07m \ge 109.14-25\\\\0.07m \ge 84.14\\\\m \ge \frac{84.14}{0.07}\\\\m \ge 1202$

This says that the least number of minutes Martina has used is 1202 minutes.

So if m was a whole number, then m could be selected from the set {1202, 1203, 1204, ...}

Side note: 1202 minutes = 1202/60 = 20.033 hours approximately.