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

19 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.

19 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 original price of refrigerator be $x$ and original price of stove be $y$.

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

Step2: We want the overall discount to be 30%.

If the overall discount is 30%, then the total discount $0.4x + 0.2y$ should be 30% of the total original price $x + y$. So, $0.4x+0.2y=0.3(x + y)$.

Step3: Expand and simplify the equation.

Expand the right - hand side: $0.4x+0.2y=0.3x + 0.3y$. Then, move the $x$ and $y$ terms to different sides: $0.4x-0.3x=0.3y - 0.2y$. This simplifies to $0.1x = 0.1y$, or $x = y$.

Answer:

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