Final answer:
The problem involves calculating the selling price of a cassette recorder based on the total profit made from selling a number of them at twice the purchase price. We set up an equation to find the purchase price, which we then double to find the selling price.
Step-by-step explanation:
The problem requires us to find out how much the store sold each cassette recorder for, given the total profit and the number of items sold and given away. To solve this, we need to calculate the cost price per recorder, the selling price per recorder, and the overall profit. Since we know the store's total profit was $1188 and the profit for each item is the selling price minus the cost price, we can set up an equation to solve for the unknowns using these relationships.
The store initially had 60 cassette recorders and gave away 3, leaving them with 57 to sell. The profit of $1188 comes entirely from selling these 57 recorders at twice their purchase price. Therefore, if we let x be the purchase price for each recorder, the selling price for each would be 2x. The profit per recorder would then be 2x - x = x. Multiplying the profit per recorder by the number of recorders sold (57), we get a total profit of 57x, which is equal to $1188.
So, we have 57x = $1188. To find x, we divide $1188 by 57, leading us to find the cost price per recorder. After finding x, we can determine the selling price by multiplying x by 2, since the selling price is twice the purchase price.