1. **Problem Statement:** We need to analyze and compare the costs of two cellphone packages: Economy and Gold, based on the number of minutes used. 2. **Formulas:** - Economy package cost: $$\text{Cost} = 20 + 1 \times n$$ where $n$ is the number of minutes. - Gold package cost: $$\text{Cost} = 40 + 0.5 \times n$$ where $n$ is the number of minutes. 3. **Calculate missing values:** - Economy package: - At $n=40$, cost is $$20 + 1 \times 40 = 60$$, so $A=60$. - Gold package: - At $n=100$, cost is $$40 + 0.5 \times 100 = 40 + 50 = 90$$ (given). - At $n=120$, cost $B = 40 + 0.5 \times 120 = 40 + 60 = 100$. 4. **Compare costs and find intersection:** Set costs equal to find when packages cost the same: $$20 + 1 \times n = 40 + 0.5 \times n$$ Simplify: $$20 + n = 40 + 0.5n$$ $$n - 0.5n = 40 - 20$$ $$0.5n = 20$$ $$n = 40$$ minutes. At $n=40$, both packages cost: $$20 + 1 \times 40 = 60$$ or $$40 + 0.5 \times 40 = 60$$. 5. **Interpretation:** - For usage less than 40 minutes, the Gold package is more expensive. - For usage more than 40 minutes, the Economy package becomes more expensive. **Final answers:** - $A=60$ (Economy cost at 40 minutes) - $B=100$ (Gold cost at 120 minutes) - Intersection at $n=40$ minutes with cost $60$. This analysis helps choose the best package based on expected usage.