SOLUTION: The manager of a discount store received two clothing shipments. The first shipment contained 10 sweaters and 20 jackets and cost $800. The second shipment, at the same prices, c

Question 194419: The manager of a discount store received two clothing shipments. The first shipment contained 10 sweaters and 20 jackets and cost $800. The second shipment, at the same prices, contained 5 sweaters and 15 jackets and costs $550. Find the cost of 1 jacket
Found 2 solutions by checkley77, doukungfoo:
Answer by checkley77(12844) (Show Source): You can put this solution on YOUR website!
20J+10S=800
15J+5S=550 MULTIPLY THIS EQUATION BY -2 & ADD.
-30J-10S=-1100
20J+10S=800
---------------------
-10J=-300
J=-300/-10
J=$30 THE PRICE OF EACH JACKET.
20*3+10X=800
600+10X=800
10X=800-600
10X=200
X=200/10
X=$20 FOR EACH SWEATER.
PROOF:
15*30+5*20=550
450+100=550
550=550

Answer by doukungfoo(195) (Show Source): You can put this solution on YOUR website!
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
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