Final answer:
The retailer's cost for the sweater is $24, calculated by dividing the retail price of $60 by the markup factor of 2.50. The sale price during a 25% off sale is $45, obtained by subtracting 25% of the retail price from the retail price itself.
Step-by-step explanation:
Let's determine the retailer's cost and the sale price of a sweater with a retail price of $60 under the conditions of a 150% markup and a regular 25% off sale. First, we calculate the cost to the retailer by taking into consideration the 150% markup. This means that the cost is less than the retail price by that markup percentage.
If 150% of the retailer's cost is the amount the price is increased by to get the retail price, we can express this as:
- Retail Price = Cost + (Cost * Markup%)
- $60 = Cost + (Cost * 1.50)
- $60 = Cost * (1 + 1.50)
- $60 = Cost * 2.50
- Cost = $60 / 2.50
- Cost = $24
Now, to find the sale price during the 25% off promotion, we calculate 25% of the $60 retail price and subtract it from the retail price:
- Sale Price = Retail Price - (Retail Price * Discount%)
- Sale Price = $60 - ($60 * 0.25)
- Sale Price = $60 - $15
- Sale Price = $45
Therefore, the retailer's cost for the sweater is $24, and the sale price of the sweater during the 25% off sale is $45.