1. **State the problem:** Matt and Ming sold small and large boxes of oranges at a fundraiser. We know: - Matt sold 3 small and 14 large boxes for a total of 203. - Ming sold 11 small and 11 large boxes for a total of 220. We need to find the cost of one small box and one large box. 2. **Set variables:** Let $x$ = cost of one small box. Let $y$ = cost of one large box. 3. **Write the system of equations:** $$\begin{cases} 3x + 14y = 203 \\ 11x + 11y = 220 \end{cases}$$ 4. **Solve the system:** Multiply the first equation by 11 and the second by 3 to align coefficients of $x$: $$\begin{cases} 11(3x + 14y) = 11 \times 203 \\ 3(11x + 11y) = 3 \times 220 \end{cases}$$ Which gives: $$\begin{cases} 33x + 154y = 2233 \\ 33x + 33y = 660 \end{cases}$$ 5. **Subtract the second equation from the first:** $$ (33x + 154y) - (33x + 33y) = 2233 - 660 $$ $$ 33x - 33x + 154y - 33y = 1573 $$ $$ 121y = 1573 $$ 6. **Solve for $y$:** $$ y = \frac{1573}{121} $$ Simplify: $$ y = 13 $$ 7. **Substitute $y=13$ into one original equation, e.g., $3x + 14y = 203$:** $$ 3x + 14(13) = 203 $$ $$ 3x + 182 = 203 $$ $$ 3x = 203 - 182 $$ $$ 3x = 21 $$ 8. **Solve for $x$:** $$ x = \frac{21}{3} $$ $$ x = 7 $$ **Final answer:** The cost of one small box is $7$ and one large box is $13$.