1. **State the problem:** We have two phone plans with different cost structures. Plan A costs $21 plus $0.13 per minute, and Plan B costs $0.17 per minute with no initial fee. We want to find the number of minutes where both plans cost the same and the cost at that point. 2. **Write the cost functions:** - Plan A cost: $C_A = 21 + 0.13m$ - Plan B cost: $C_B = 0.17m$ where $m$ is the number of minutes. 3. **Set the costs equal to find the break-even point:** $$21 + 0.13m = 0.17m$$ 4. **Solve for $m$:** Subtract $0.13m$ from both sides: $$21 = 0.17m - 0.13m$$ $$21 = 0.04m$$ Divide both sides by $0.04$: $$m = \frac{21}{0.04} = 525$$ 5. **Find the cost at $m=525$ minutes:** Use either plan's cost function, for example Plan B: $$C_B = 0.17 \times 525 = 89.25$$ **Answer:** - The plans cost the same at **525 minutes**. - The cost at that time is **89.25**. This means if you talk for 525 minutes, both plans will cost you the same amount, $89.25.