1. **State the problem:** We need to find the number of minutes at which the cost of the Gold Plan equals the cost of the Platinum Plan. 2. **Define the cost functions:** - Gold Plan cost: $20 + 0.05m$ where $m$ is the number of minutes. - Platinum Plan cost: $30$ (fixed, unlimited usage). 3. **Set the costs equal to find the break-even point:** $$20 + 0.05m = 30$$ 4. **Solve for $m$:** $$0.05m = 30 - 20$$ $$0.05m = 10$$ 5. **Divide both sides by 0.05:** $$m = \frac{10}{0.05}$$ $$m = 10 \times \frac{1}{0.05}$$ $$m = 10 \times 20$$ $$m = 200$$ 6. **Interpretation:** At 200 minutes, the cost of both plans is the same. **Final answer:** The Gold Plan and Platinum Plan cost the same at **200 minutes**.