The wholesale cost of a video game is $459.45. The original markup was 51% based on selling price. Find the final sale price after the following series of price changes: a markup of 24%, a markup of 17%, and a markdown of 10%.

To find the final sale price after the series of price changes, we need to apply each markup and markdown one by one to the previous price.

Let's start with the original wholesale cost of the video game, which is $459.45. The original markup of 51% based on selling price means the selling price was increased by 51% of the selling price.

To calculate the selling price after the 51% markup, we can use the formula:

Selling Price = Wholesale Cost + (Markup % * Wholesale Cost)

Substituting the values in the formula, we have:

Selling Price = $459.45 + (51/100 * $459.45)
Selling Price = $459.45 + ($234.39)
Selling Price = $693.84

Now, let's apply the subsequent price changes one by one.

1. Markup of 24%:
To calculate the new selling price after a 24% markup, we use the formula:

Selling Price = Previous Selling Price + (Markup % * Previous Selling Price)

Substituting the values in the formula, we have:

Selling Price = $693.84 + (24/100 * $693.84)
Selling Price = $693.84 + ($166.72)
Selling Price = $860.56

2. Markup of 17%:
To calculate the new selling price after a 17% markup, we use the formula:

Selling Price = Previous Selling Price + (Markup % * Previous Selling Price)

Substituting the values in the formula, we have:

Selling Price = $860.56 + (17/100 * $860.56)
Selling Price = $860.56 + ($146.49)
Selling Price = $1007.05

3. Markdown of 10%:
To calculate the final sale price after a 10% markdown, we use the formula:

Final Sale Price = Selling Price - (Markdown % * Selling Price)

Substituting the values in the formula, we have:

Final Sale Price = $1007.05 - (10/100 * $1007.05)
Final Sale Price = $1007.05 - ($100.71)
Final Sale Price = $906.34

Therefore, the final sale price after the series of price changes is $906.34.