20. 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.
Answer: A,B,C
x could be 50, 75, or 100 dollars.
The profit from selling the last sofa must exceed 15 percent of the wholesale price of $400, which amounts to $60. Therefore, the reduced selling price must be at least $460 for the profit to meet this requirement. This means that values of x that result in a selling price of at least $460 are acceptable.
A) 50
If x is 50, the selling price becomes $560 - $50 = $510. The profit from this sale is $510 - $400 = $110, which is greater than $60. Therefore, 50 is a valid option.
B) 75
If x is 75, the selling price is $560 - $75 = $485. The profit on this sale is $485 - $400 = $85, which also exceeds $60. Thus, 75 is a valid option.
C) 100
With x equal to 100, the selling price would be $560 - $100 = $460. The profit in this case would be $460 - $400 = $60, which meets the requirement of being more than 15 percent of the wholesale price. Therefore, 100 is a valid option.
D) 125
If x is 125, the selling price becomes $560 - $125 = $435. The profit here would be $435 - $400 = $35, which is less than $60. Thus, 125 is not a valid option.
Conclusion
The values of x that allow the store's profit to exceed 15 percent of the wholesale price are 50, 75, and 100. Option D fails to meet the profit requirement, while the other options ensure the profit remains above the necessary threshold. Hence, the correct values of x are definitively 50, 75, and 100 dollars.