1. **Problem Statement:** Hank’s Ice Cream Shop sells single-scoop cones for 2.00 each and double-scoop cones for 2.50 each. He sold 230 cones total and made 498 in sales. We want to analyze and solve the system of equations representing this situation. 2. **Explain the equations:** - The equation $x + y = 230$ means the total number of cones sold is 230, where $x$ is the number of single-scoop cones and $y$ is the number of double-scoop cones. - The equation $2x + 2.5y = 498$ represents the total sales amount. Each single-scoop cone costs 2.00, so $2x$ is the total from single-scoop cones. Each double-scoop cone costs 2.50, so $2.5y$ is the total from double-scoop cones. Their sum is 498. 3. **Variables meaning:** - $x$ represents the number of single-scoop cones sold. - $y$ represents the number of double-scoop cones sold. 4. **Solve the system using substitution:** - From the first equation, express $x$ in terms of $y$: $$x = 230 - y$$ - Substitute into the second equation: $$2(230 - y) + 2.5y = 498$$ - Distribute: $$460 - 2y + 2.5y = 498$$ - Combine like terms: $$460 + 0.5y = 498$$ - Subtract 460 from both sides: $$0.5y = 498 - 460$$ $$0.5y = 38$$ - Divide both sides by 0.5: $$y = \cancel{0.5} \frac{38}{\cancel{0.5}} = 76$$ - Substitute $y=76$ back into $x = 230 - y$: $$x = 230 - 76 = 154$$ 5. **Interpretation of the solution:** - Hank sold 154 single-scoop cones and 76 double-scoop cones that day. **Final answer:** $x=154$, $y=76$ cones sold.