uations with the Variable on Both Sides - Item 32972 One phone company charges a flat fee of \( \$ 35 \), plus \( \$ 0.15 \) for each minute. The other phone company charges a flat fee of \( \$ 20 \), plus \( \$ 0.25 \) for each minute. Which equation can be used to solve for the number of minutes, \( m \), for which the companies charge the same amount?

To determine the number of minutes \( m \) at which both phone companies charge the same amount, you can set up an equation by equating their total costs. **Let’s define the costs for each company:** 1. **Company A:** - **Flat fee:** \$35 - **Cost per minute:** \$0.15 - **Total cost for \( m \) minutes:** \( 35 + 0.15m \) 2. **Company B:** - **Flat fee:** \$20 - **Cost per minute:** \$0.25 - **Total cost for \( m \) minutes:** \( 20 + 0.25m \) **Setting the total costs equal to each other:** \[ 35 + 0.15m = 20 + 0.25m \] **This equation can be used to solve for the number of minutes \( m \) where both companies charge the same amount.** **Steps to Solve (Optional):** 1. **Subtract \$20 from both sides:** \[ 15 + 0.15m = 0.25m \] 2. **Subtract \( 0.15m \) from both sides:** \[ 15 = 0.10m \] 3. **Divide both sides by 0.10:** \[ m = \frac{15}{0.10} = 150 \] **Conclusion:** At **150 minutes**, both phone companies will charge the same total amount. **Final Equation:** \[ 35 + 0.15m = 20 + 0.25m \]