A furniture store purchased sofas for a wholesale price of $400 each and sold most of them for a retail price of $560 each. In a summer sale, the retail price of the last few sofas was reduced by x dollars, and they were sold at this reduced price. The store's profit from selling the last sofa was more than 15 percent of its wholesale price. Which of the following could be the value of x? Indicate all such values.
Values of x that could result in a profit greater than 15 percent of the wholesale price are 50, 75, and 100.
To determine the possible values of x, we first calculate the required profit threshold. A profit of more than 15 percent of the wholesale price ($400) equates to more than $60, meaning the sale price must exceed $460. Therefore, we can find which reductions in price still allow for a profit above this threshold.
If x is 50, the reduced selling price is $560 - $50 = $510. The profit would then be $510 - $400 = $110, which is more than $60, meeting the profit requirement.
With x set at 75, the selling price becomes $560 - $75 = $485. The profit in this case is $485 - $400 = $85, which also exceeds the necessary $60 profit threshold.
If x equals 100, the selling price is $560 - $100 = $460. The profit would then be $460 - $400 = $60, which is exactly the minimum required and thus qualifies as greater than 15 percent.
Setting x to 125 results in a selling price of $560 - $125 = $435. The profit in this scenario is $435 - $400 = $35, which does not meet the required profit of more than $60, disqualifying this option.
The possible values of x that lead to a profit exceeding 15 percent of the wholesale price are 50, 75, and 100. These options maintain a selling price that results in a sufficient profit margin, whereas a reduction of 125 fails to meet the profit requirement. Understanding the relationship between selling price, wholesale cost, and profit margin is essential for pricing strategy in retail.
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