Sullivan's Handbags mark up their bags at 45% of the selling price. Pat Sullivan saw a bag at a trade show that she would sell to her customers for $85. What is the most she could pay for the bag and still retain the 45% markup of the selling price?

To find out the most Pat Sullivan could pay for the bag, we need to first determine the selling price after the 45% markup.

Let's assume the original cost price of the bag is X dollars.

To calculate the selling price after the 45% markup, we can use the following formula:

Selling Price = Cost Price + (Markup Percentage * Cost Price)

In this case, the markup percentage is 45%, which can be written as 0.45. So the formula becomes:

Selling Price = X + (0.45 * X)

According to the given information, the selling price is $85. Therefore, we can write the equation as:

$85 = X + (0.45 * X)

To solve this equation for X (the original cost price), we can simplify it as follows:

$85 = 1.45 * X

Dividing both sides of the equation by 1.45:

X = $85 / 1.45 ≈ $58.62

So, the original cost price of the bag is approximately $58.62. This means that the most Pat Sullivan could pay for the bag and still retain the 45% markup is $58.62.