A leather recliner is on sale for 30% less than its original price. A consumer has a coupon that saves an additional 25% off of the sale price. If the consumer pays $237 for the recliner, what is the original price of the recliner to the nearest dollar?

Rationale

The original price of the recliner is approximately $451.

The problem involves two successive discounts: first, a 30% discount off the original price, then a 25% discount off the sale price. To find the original price, we need to reverse these discounts starting from the final price paid by the consumer.

A ($451) CORRECT

To reverse the discounts, we first consider the 25% coupon discount. If $237 is 75% (100% - 25%) of the sale price, then the sale price is $237 / 0.75 = $316. Next, we reverse the initial 30% discount by considering the sale price as 70% (100% - 30%) of the original price. So, the original price is $316 / 0.7, which is approximately $451.

B ($527) YOUR ANSWER

This value is incorrect because it's higher than the calculated original price. If the recliner was originally priced at $527, the consumer would have ended up paying more than $237 after applying the two discounts.

C ($316) YOUR ANSWER

This value is the sale price of the recliner after the initial 30% discount, not the original price. If the recliner was originally priced at $316, the final price after both discounts would have been less than $237.

D ($431) YOUR ANSWER

This value is incorrect because it's lower than the calculated original price. If the recliner was originally priced at $431, the final price after both discounts would have been less than $237.

Conclusion

To find the original price after successive discounts, we need to reverse the discounts, starting from the final price. In this case, the original price of the leather recliner, before any discounts, is approximately $451. This is calculated by reversing a 25% discount on the final price of $237 to find the sale price, and then reversing a 30% discount on the sale price to find the original price. Any other price would result in a final price that is either more or less than the $237 paid by the consumer.

A leather recliner is on sale for 30% less than its original price. A consumer has a coupon that saves an additional 25% off of the sale price. If the consumer pays $237 for the recliner, what is the original price of the recliner to the nearest dollar?

The original price of the recliner is approximately $451.

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