The expression below represents the cost, c, of an item that is on sale for 25% off.
Which expression is also equivalent to the cost of the item? 0.75c 1 – 0.75c 0.25c 1 – 0.25c
The Correct Answer and Explanation is:
The correct answer is: 0.75c
Explanation
The original expression given is:
c − 0.25c
This expression represents the cost of an item after a 25% discount. In this case, c represents the original price of the item, and 0.25c is 25% of that price. When an item is discounted by 25%, you’re paying only the remaining 75% of the original price.
To simplify the expression: c−0.25c=(1−0.25)c=0.75cc – 0.25c = (1 – 0.25)c = 0.75c
So, instead of subtracting 25% of the cost, we can directly multiply the original cost by 0.75. This is a quicker way to compute sale prices: multiplying by the percentage you’re actually paying.
Now, let’s look at the answer choices:
- 0.75c – This is correct. It represents 75% of the original price, which is what you pay after a 25% discount.
- 1 − 0.75c – This doesn’t make sense in this context. You’re not subtracting 75% of c from 1. This expression does not represent the correct discounted price.
- 0.25c – This represents 25% of the original price, which is the amount of the discount, not the final price paid.
- 1 − 0.25c – This is also incorrect. Subtracting 0.25c from 1 doesn’t give a meaningful result in terms of finding a sale price.
In summary, when an item is on sale for 25% off, you pay 75% of the original price. That means you multiply the original cost, c, by 0.75. So, the expression 0.75c is equivalent to c − 0.25c, and correctly represents the cost after the discount.
