A leather recliner is on sale for 30% less than its original price. A consumer has a coupon that saves an additional of 25% off of 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.
$316
B.
$431
C.
$451
D.
$527
The correct answer and Explanation is :
To determine the original price of the recliner, let’s denote the original price as ( P ). The recliner is first discounted by 30%, which means the sale price is 70% of the original price. The formula for the sale price ( S ) can be written as:
[ S = P \times (1 – 0.30) ]
[ S = P \times 0.70 ]
Next, the consumer uses a coupon that offers an additional 25% discount on the sale price. This means the final price the consumer pays is 75% of the sale price. Let’s denote the final price as ( F ):
[ F = S \times (1 – 0.25) ]
[ F = S \times 0.75 ]
Substituting the expression for ( S ) into the equation for ( F ):
[ F = (P \times 0.70) \times 0.75 ]
[ F = P \times 0.70 \times 0.75 ]
[ F = P \times 0.525 ]
We know the consumer pays $237, so we set up the equation:
[ P \times 0.525 = 237 ]
To find ( P ), we solve for ( P ) by dividing both sides by 0.525:
[ P = \frac{237}{0.525} ]
[ P \approx 452.38 ]
Rounding to the nearest dollar, the original price ( P ) is approximately $452.
Thus, the correct answer is closest to option C:
C. $451