When winter jackets are sold for $250 each, an outdoors store can sell 110 in a season. For every $25 nicrease in the price, the number sold drops by 10. If the total sales revenue is $22500, how many of these jackets were sold?

To determine how many jackets were sold, we can start by using the given information and forming equations to solve the problem.

Let's denote the initial price of a winter jacket as "P" and the number of jackets sold as "N."

Given information:
- The initial price of a winter jacket is $250.
- The outdoors store can sell 110 jackets in a season.
- For every $25 increase in price, the number of jackets sold drops by 10.
- The total sales revenue is $22,500.

From the given information, we can derive the following equations:

1. The total sales revenue is calculated by multiplying the price per jacket by the number of jackets sold:
Total Revenue = Price per Jacket × Number of Jackets Sold
$22,500 = P × N ... equation (1)

2. The relationship between the price increase and the corresponding decrease in the number of jackets sold can be expressed as follows:
Number of Jackets Sold = Initial Number of Jackets Sold - (Price Increase / $25) × 10
N = 110 - (P - $250) / $25 × 10 ... equation (2)

Now we can solve the system of equations (1) and (2) simultaneously.

Substitute the value of N from equation (2) into equation (1):
$22,500 = P × (110 - (P - $250) / $25 × 10)

Simplify the equation:
$22,500 = P × (110 - 10(P - $250) / $25)

Multiply both sides of the equation by $25 to eliminate the fraction:
$562,500 = 25P × (110 - 10(P - $250))

Expand and simplify further:
$562,500 = 2,750P - 250P^2 + $2,750,000

Rearrange the equation to a quadratic form:
250P^2 - 2,750P - $2,187,500 = 0

Now we can solve this quadratic equation to find the values of P (price per jacket). Using the quadratic formula, we get:
P = [2,750 ± √(2,750^2 - 4 × 250 × (-$2,187,500))] / (2 × 250)

Simplifying further, we get two possible values for P:
P ≈ $40.357 or P ≈ $17.643

Since the initial price of a winter jacket cannot be less than $250, we can discard the second solution, P ≈ $17.643.

Let's substitute the value of P, which is approximately $40.357, back into equation (2) to find the number of jackets sold (N):
N = 110 - ($40.357 - $250) / $25 × 10
N ≈ 110 - ($40.357 - $250) / $25 × 10
N ≈ 110 - $2093.93 / $25 × 10
N ≈ 110 - $83.7572 × 10
N ≈ 110 - 837.572
N ≈ -727.572

Since the number of jackets sold cannot be negative, we can conclude that there is an error in the calculations or the given information.

Please double-check the values and ensure all information is accurate.