Question

question #1
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?

○ the sales prices of the refrigerator and the stove are the same.

○ the original prices of the refrigerator and the stove are the same.

○ the sale price of the refrigerator was twice the sale price of the stove.

○ the original price of the refrigerator was twice the original price of the stove.

Explanation:

Step1: Define variables for original prices

Let $R$ = original price of refrigerator, $S$ = original price of stove.

Step2: Calculate total original cost

Total original cost: $R + S$

Step3: Calculate total sale cost

Refrigerator sale price: $0.6R$ (40% off = 60% of original).
Stove sale price: $0.8S$ (20% off = 80% of original).
Total sale cost: $0.6R + 0.8S$

Step4: Set up 30% overall discount condition

30% off total original cost = 70% of total original cost:
$0.6R + 0.8S = 0.7(R + S)$

Step5: Simplify the equation

Expand right side: $0.6R + 0.8S = 0.7R + 0.7S$
Rearrange terms: $0.8S - 0.7S = 0.7R - 0.6R$
Simplify: $0.1S = 0.1R$ → $R = S$

Answer:

The original prices of the refrigerator and the stove are the same.