Final answer:
To maintain a 57% average mark-up, the buyer must set the average retail price for each wool jacket at $25.1, after calculating the total cost and mark-up for silk jackets.
Step-by-step explanation:
The question involves calculating the average retail price for wool jackets to maintain a 57% mark-up based on the cost and retail price of silk jackets. First, we calculate the total cost and desired selling price for the silk jackets to find the overall mark-up needed for all jackets combined. Then, using this data, we can find the required average selling price for the wool jackets to meet the average mark-up percentage.
Total cost of silk jackets = 50 * $78 = $3900
Total selling price of silk jackets = 50 * $175 = $8750
Total profit from silk jackets = $8750 - $3900 = $4850
Mark-up on silk jackets = ($4850 / $3900) * 100 = 124.36%
Total cost of wool jackets = 38 * $60 = $2280
The total mark-up desired across all jackets = 57% * (Total Cost of all jackets) = 57% * ($3900 + $2280) = 57% * $6180 = $3523.6
The total desired selling price for all jackets = Total Cost of all jackets + Total mark-up = $6180 + $3523.6 = $9703.6
Since we already have the selling price for silk jackets, we can subtract this to find the required total selling price for wool jackets:
Total desired selling price for wool jackets = Total desired selling price for all jackets - Total selling price of silk jackets = $9703.6 - $8750 = $953.6
Finally, we find the average selling price per wool jacket:
Average retail price for each wool jacket = Total desired selling price for wool jackets / Number of wool jackets = $953.6 / 38 = $25.1