Alfonso went to famous sam's appliances 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.

Option: b is the correct answer.

b)  The original prices of the refrigerator and the stove were the same.

Step-by-step explanation:

Let the original price of refrigerator be: $ x

and the original price of stove be: $ y

Hence, the total original price of both is: $ (x+y)

Now, it is given that:

     This means that the refrigerator was sold at:

                (100-40)% of x.

                i.e. 60% of x

               i.e. 0.60 of x

    i.e. The sale price of refrigerator is: 0.60 x

Similarly it is given that:

This means that the stove was sold at:

                (100-20)% of y.

                i.e. 80% of y

               i.e. 0.80 of y.

 i.e. The sale price of stove is: 0.80 y

Hence, the total sale price of both the items is: 0.60x+0.80y

Also, it is given that:

Alfonso received a 30% overall discount on the refrigerator and the stove together.

i.e.

Total Sale Price=70% of Total original price.

i.e. Total sale Price=0.70×Total original Price

i.e    0.60x+0.80y=0.70(x+y)

i.e.   0.60x+0.80y=0.70x+0.70y

i.e.   0.80y-0.70y=0.70x-0.60x

i.e.    0.10y=0.10x

i.e.     y=x

Hence, the original price of both the items were same.