The combined original price for a mirror and a vase is $ 60 . After a

Choice C is correct. It’s given that $m$ represents the original price, in dollars, of the mirror, and $v$ represents the original price, in dollars, of the vase. It's also given that the combined original price for the mirror and the vase is $\$60$. This can be represented by the equation $m+v=60$. After a $25\%$ discount to the mirror is applied, the sale price of the mirror is $75\%$ of its original price. This can be represented by the expression $0.75m$. After a $45\%$ discount to the vase is applied, the sale price of the vase is $55\%$ of its original price. This can be represented by the expression $0.55v$. It’s given that the combined sale price for the two items is $\$39$. This can be represented by the equation $0.75m+0.55v=39$. Therefore, the system of equations consisting of the equations $m+v=60$ and $0.75m+0.55v=39$ gives the original price $m$, in dollars, of the mirror and the original price $v$, in dollars, of the vase.

Choice A is incorrect. The second equation in this system of equations represents a $45\%$ discount to the mirror and a $25\%$ discount to the vase.

Choice B is incorrect. The second equation in this system of equations represents a $55\%$ discount to the mirror and a $75\%$ discount to the vase.

Choice D is incorrect. The second equation in this system of equations represents a $75\%$ discount to the mirror and a $55\%$ discount to the vase.