Final answer:
To find the initial markup on the doll as a percentage of cost, the cost is first estimated per dollar of retail and then applied to the actual cost, followed by calculating the markup amount, and finally determining the percentage of markup over cost, which is approximately 48.2%.
Step-by-step explanation:
To calculate the initial markup as a percentage of cost for the limited edition Alice in Wonderland dolls, we need to understand the relationship between cost, retail price, and markup. Given that the initial markup as a percentage of retail is 48.15%, we can infer that for every $1.00 of retail price, there is $0.4815 of markup. To find the cost of the doll, we divide the retail price, which we can consider as $1.00 for simplicity, by 1 plus the markup percentage in decimal form. This gives us the cost equal to $1.00 / (1 + 0.4815).
The cost is approximately $0.6754 per dollar of retail. Since we know the actual cost of the doll is $125, we will use this figure. The retail price is then $125 / $0.6754 = $185.09 approximately. Next, to find the markup amount, we deduct the cost from the retail price, which gives $185.09 - $125 = $60.09. Finally, to get the markup as a percentage of the cost, we divide the markup amount by the cost and multiply by 100, resulting in ($60.09 / $125) * 100 = 48.1%, which is approximately 48.2% when rounded to one decimal place.