1. **State the problem:** We need to find the system of equations representing the original prices of a mirror ($m$) and a vase ($v$) given their combined original price and the combined sale price after discounts. 2. **Given:** - Original combined price: $m + v = 60$ - Mirror discount: 25%, so sale price of mirror is $75\%$ of $m$, i.e., $0.75m$ - Vase discount: 45%, so sale price of vase is $55\%$ of $v$, i.e., $0.55v$ - Combined sale price: $0.75m + 0.55v = 39$ 3. **Form the system of equations:** $$\begin{cases} m + v = 60 \\ 0.75m + 0.55v = 39 \end{cases}$$ 4. **Explanation:** - The first equation states the total original price. - The second equation accounts for the discounts applied to each item and their combined sale price. 5. **Match with options:** This corresponds to option C. **Final answer:** Option C