1. **State the problem:** You are comparing two cell phone plans. The first plan charges 23 cents per minute, and the second plan charges a monthly fee of 49.95 plus 11 cents per minute. We want to find the number of minutes $t$ where both plans cost the same. 2. **Write the cost equations:** - First plan cost: $C_1 = 0.23t$ - Second plan cost: $C_2 = 49.95 + 0.11t$ 3. **Set the costs equal to find $t$:** $$0.23t = 49.95 + 0.11t$$ 4. **Solve for $t$:** Subtract $0.11t$ from both sides: $$0.23t - 0.11t = 49.95$$ $$\cancel{0.23}t - \cancel{0.11}t = 49.95$$ $$0.12t = 49.95$$ 5. **Divide both sides by 0.12:** $$t = \frac{49.95}{0.12}$$ 6. **Calculate the value:** $$t = 416.25$$ 7. **Interpretation:** If you talk for approximately 416.3 minutes, both plans will cost the same. **Final answer:** - $C_1 = 0.23t$ - $C_2 = 49.95 + 0.11t$ - Equal cost at $t = 416.3$ minutes (rounded to one decimal place).