A leather recliner is on sale for 30% less than its original price. A consumer has a coupon that serves an additional 25% off the sale price. If the consumer pays $ 237 for the recliner, which of the following is the original price of the recliner to the nearest dollar?
A.
$527
B.
$316
C.
$432
D.
$451
The Correct Answer and Explanation is :
To determine the original price of the leather recliner, we need to backtrack from the final price paid by the consumer, which is $237. The process involves working through the discount percentages to find the original price.
Let’s denote the original price of the recliner as PPP.
- Applying the First Discount: The recliner is on sale for 30% less than its original price. This means the sale price is 70% of the original price. Therefore, the sale price can be expressed as:Sale Price=0.70×P\text{Sale Price} = 0.70 \times PSale Price=0.70×P
- Applying the Second Discount: The consumer has a coupon for an additional 25% off the sale price. Thus, the final price is 75% of the sale price. Therefore, the final price can be expressed as:Final Price=0.75×(Sale Price)\text{Final Price} = 0.75 \times (\text{Sale Price})Final Price=0.75×(Sale Price)Substituting the expression for the sale price:Final Price=0.75×(0.70×P)\text{Final Price} = 0.75 \times (0.70 \times P)Final Price=0.75×(0.70×P)Simplifying this, we get:Final Price=0.75×0.70×P=0.525×P\text{Final Price} = 0.75 \times 0.70 \times P = 0.525 \times PFinal Price=0.75×0.70×P=0.525×P
- Solving for the Original Price: We know that the final price paid by the consumer is $237. Therefore:0.525×P=2370.525 \times P = 2370.525×P=237Solving for PPP:P=2370.525≈452.57P = \frac{237}{0.525} \approx 452.57P=0.525237≈452.57Rounding this value to the nearest dollar gives us an original price of approximately $453.
Among the provided options, the closest value to this is:
D. $451
Thus, the original price of the recliner to the nearest dollar is $451.