alfonso went to famous sams appliance store and purchased a refrigerator and a stove. the sale price of the…

alfonso went to famous sams appliance store and purchased a refrigerator and a stove. the sale price of the refrigerator was 40% off the original price and the sale price of the stove was 20% off the original price. which statement must be true to conclude that alfonso received a 30% overall discount on the refrigerator and the stove together? a the sale prices of the refrigerator and the stove were the same. b the original prices of the refrigerator and the stove were the same. c the sale price of the refrigerator was twice the sale price of the stove. d the original price of the refrigerator was twice the original price of the stove.

alfonso went to famous sams appliance store and purchased a refrigerator and a stove. the sale price of the refrigerator was 40% off the original price and the sale price of the stove was 20% off the original price. which statement must be true to conclude that alfonso received a 30% overall discount on the refrigerator and the stove together? a the sale prices of the refrigerator and the stove were the same. b the original prices of the refrigerator and the stove were the same. c the sale price of the refrigerator was twice the sale price of the stove. d the original price of the refrigerator was twice the original price of the stove.

Answer

Explanation:

Step1: Let the original price of the refrigerator be $x$ and the original price of the stove be $y$.

The sale - price of the refrigerator is $(1 - 0.4)x=0.6x$, and the sale - price of the stove is $(1 - 0.2)y = 0.8y$. The total original price is $x + y$, and the total sale price is $0.6x+0.8y$.

Step2: If the overall discount is 30%, then the total sale price is $(1 - 0.3)(x + y)=0.7(x + y)$.

So we set up the equation $0.6x+0.8y=0.7(x + y)$.

Step3: Expand the right - hand side of the equation.

$0.6x+0.8y=0.7x + 0.7y$.

Step4: Rearrange the terms.

$0.8y-0.7y=0.7x - 0.6x$. $0.1y = 0.1x$. $x=y$.

Answer:

B. The original prices of the refrigerator and the stove were the same.