1. **State the problem:** Matt and Ming sold small and large boxes of oranges at a fundraiser. Matt sold 3 small and 14 large boxes for 203, and Ming sold 11 small and 11 large boxes for 220. We need to find the cost of one small box and one large box. 2. **Define variables:** Let $x$ be the cost of one small box. Let $y$ be the cost of one large box. 3. **Set up the equations from the given information:** From Matt's sales: $$3x + 14y = 203$$ From Ming's sales: $$11x + 11y = 220$$ 4. **Solve the system of equations:** Multiply the first equation by 11 and the second by 14 to align $y$ coefficients: $$11(3x + 14y) = 11 \times 203 \Rightarrow 33x + 154y = 2233$$ $$14(11x + 11y) = 14 \times 220 \Rightarrow 154x + 154y = 3080$$ 5. **Subtract the first from the second to eliminate $y$:** $$ (154x + 154y) - (33x + 154y) = 3080 - 2233 $$ $$ 121x = 847 $$ 6. **Solve for $x$: $$ x = \frac{847}{121} = 7 $$** 7. **Substitute $x=7$ back into one of the original equations, say Matt's:** $$3(7) + 14y = 203$$ $$21 + 14y = 203$$ $$14y = 203 - 21 = 182$$ $$y = \frac{182}{14} = 13$$ 8. **Final answer:** The cost of one small box is $7$ and one large box is $13$.