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Algebra / Systems of two linear equations in two variables Difficulty: Medium

The combined original price for a mirror and a vase is $dollar sign 60$ . After a $25 percent sign$ discount to the mirror and a $45 percent sign$ discount to the vase are applied, the combined sale price for the two items is $dollar sign 39$ . Which system of equations gives the original price $m$ , in dollars, of the mirror and the original price $v$ , in dollars, of the vase?

$m + v = 60$

$0.55 m + 0.75 v = 39$

$m + v = 60$

$0.45 m + 0.25 v = 39$

$m + v = 60$

$0.75 m + 0.55 v = 39$

$m + v = 60$

$0.25 m + 0.45 v = 39$

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Explanation

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 $dollar sign 60$ . This can be represented by the equation $m + v = 60$ . After a $25 percent sign$ discount to the mirror is applied, the sale price of the mirror is $75 percent sign$ of its original price. This can be represented by the expression $0.75 m$ . After a $45 percent sign$ discount to the vase is applied, the sale price of the vase is $55 percent sign$ of its original price. This can be represented by the expression $0.55 v$ . It’s given that the combined sale price for the two items is $dollar sign 39$ . This can be represented by the equation $0.75 m + 0.55 v = 39$ . Therefore, the system of equations consisting of the equations $m + v = 60$ and $0.75 m + 0.55 v = 39$ 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 $45 percent sign$ discount to the mirror and a $25 percent sign$ discount to the vase.

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

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