Solve the problem. During the sale price of the sofa was discounted by 30%.Determine which of the statements below is true. A.the sale price of the sofa is 70% of the regular price. B.the sale price of the sofa is 70% less than the regular price. C. The sale price of the sofa is 30% of the regular price.D. The regular price of the sofa is 101% of the sale price
A. the sale price of the sofa is 70% of the regular price.
Let's solve the problem step-by-step:
Given:
- The sale price of the sofa was discounted by 30%.
To find the correct statement, let's analyze each option:
A. The sale price of the sofa is 70% of the regular price.
This statement is not true since the sale price is discounted, not multiplied by 70%.
B. The sale price of the sofa is 70% less than the regular price.
This statement is not true since the discount is 30%, not 70%.
C. The sale price of the sofa is 30% of the regular price.
This statement is true since the discount is 30%. The sale price is the regular price minus the 30% discount, which means it is 100% - 30% = 70% of the regular price.
D. The regular price of the sofa is 101% of the sale price.
This statement is not true since the sale price is discounted, not increased by 1%.
Therefore, the correct statement is C. The sale price of the sofa is 30% of the regular price.
To solve this problem, we need to understand the concept of a discount. A discount is a reduction in price from the original or regular price. In this case, the sale price of the sofa was discounted by 30%.
To determine the true statement, let's analyze the options:
A) The sale price of the sofa is 70% of the regular price.
This statement is not true. If the sale price is 70% of the regular price, it means that the discount is 30%, which contradicts the given information that the sofa was discounted by 30%.
B) The sale price of the sofa is 70% less than the regular price.
This statement is also not true. If the sale price is 70% less than the regular price, it means that the discount is 70%, which again contradicts the given information that the sofa was discounted by 30%.
C) The sale price of the sofa is 30% of the regular price.
This statement is true. Since the sale price was discounted by 30%, it means that the sale price is equal to 70% (100% - 30%) of the regular price.
D) The regular price of the sofa is 101% of the sale price.
This statement is not true. If the regular price is 101% of the sale price, it means that the discount is only 1%, which contradicts the given information that the sofa was discounted by 30%.
Therefore, the true statement is: C. The sale price of the sofa is 30% of the regular price.