Question 194419
Lets start out by defining some variables. 
we will call the price of the sweaters x
and the price of the jackets y
We are told that 10 sweaters and 20 jackets and cost $800
write this as an equation using the variables x and y
10x + 20y = 800

Now the next part of the problem tells us that 5 sweaters and 15 jackets and costs $550. So write this as an equation:
5x + 15y = 550

Ok so we have a system of equations 
10x + 20y = 800
5x + 15y = 550

The problem ask us to find the cost of 1 jacket. We stated in the beginning that the price of a jacket is equal to y. So we need to solve for y.
start with the first equation and set it equal to x
10x + 20y = 800
10x = 800 -20y  'subtract 20y from both sides
x = 80 - 2y 'divide both sides by 10
Now since we have shown that x is equal to 80 - 2y we can substitute the x in the second equation with 80 - 2y

5x + 15y = 550
5(80 - 2y) + 15y = 550 'replace x with 80 - 2y
400 - 10y + 15y = 550 ' multiply 5 times 80 -2y
-10y + 15y = 150 'subtract 400 from both sides
5y = 150 'combine like terms
y = 30 'divide both sides by 5

so the cost of 1 jacket is $30.00