Questions: For her phone service, Leila pays a monthly fee of 30, and she pays an additional 0.06 per minute of use. The least she has been charged in a month is 109.02. 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.

For her phone service, Leila pays a monthly fee of 30, and she pays an additional 0.06 per minute of use. The least she has been charged in a month is 109.02.

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.

Transcript text: For her phone service, Leila pays a monthly fee of $\$ 30$, and she pays an additional $\$ 0.06$ per minute of use. The least she has been charged in a month is \$109.02. 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 $m$.

Solution

Solution Steps

Step 1: Define the inequality

Leila's total monthly cost consists of a fixed fee of \$30 plus \$0.06 per minute of use. The least she has been charged is \$109.02. This can be expressed as: \[ 30 + 0.06m \geq 109.02 \]

Step 2: Subtract the fixed fee

Subtract the fixed fee of \$30 from both sides of the inequality to isolate the term with $ m $: \[ 0.06m \geq 109.02 - 30 \] \[ 0.06m \geq 79.02 \]

Step 3: Solve for $ m $

Divide both sides of the inequality by \$0.06 to solve for $ m $: \[ m \geq \frac{79.02}{0.06} \] \[ m \geq 1317 \]