Question

The expression (x - 0.35x) represents 35% off the cost of item x. How is this equivalent to multiplying x by 0.65?

Answer 1

Subtracting 35% of a price from the original is the same as multiplying the price by 65%. This is because you can factor out the original price from the expression (x - 0.35x), which simplifies to x(1 - 0.35) or x(0.65), indicating a 65% remaining price.

Step-by-step explanation:

The expression (x - 0.35x) represents the original price x minus 35% of the original price x, which gives the discounted price of the item. To see how this is equivalent to multiplying x by 0.65, we can factor out x from the expression:

• x - 0.35x = x(1 - 0.35)
• = x(0.65)

This shows that subtracting 35% is the same as multiplying by 65%, or 0.65, which represents the remaining percentage of the price after the discount. This is a common percentage calculation in discount problems.

Answer 2

It is equivalent.

Step-by-step explanation:

(x-0.35x) is (Total price-0.35 × the original price)=0.65×