9. A book is on sale for 25% off. If the original price of the book was D dollars, what is the sale price, in dollars, in terms of D?
Answer: C
The sale price of the book is 0.75D.
To find the sale price of the book after a 25% discount, we calculate 75% of the original price. This can be represented as 0.75 times the original price D, resulting in a sale price of 0.75D.
A) D - 25
This option suggests subtracting a fixed amount of 25 from the original price D. However, the problem states a percentage discount (25%), not a fixed dollar amount, making this interpretation incorrect.
B) 7.5D
This choice implies multiplying the original price D by 7.5, which would suggest a significant increase rather than a discount. Since we are looking for a sale price after a discount, this option is incorrect.
C) 0.75D
This option accurately reflects the sale price after applying a 25% discount to the original price D. By taking 75% of D (which is 100% - 25%), we arrive at the correct calculation of the sale price as 0.75D.
D) 0.25D
This option represents 25% of the original price D, which is not the sale price but rather the amount of the discount itself. Therefore, this choice does not answer the question regarding the sale price.
Conclusion
The correct option, 0.75D, provides the accurate calculation of the sale price after a 25% discount on the original price D. Other options either misinterpret the percentage discount as a fixed amount or incorrectly calculate the sale price, thereby failing to address the question accurately. Thus, 0.75D is definitively the correct answer.