The manager of a discount clothing store received two shipments. The first shipment contained 10 identical sweaters and 20 identical jackets and cost $800. The second shipment contained 5 identical sweaters and 15 identical jackets. The cost of the second shipment was $550. The cost per sweater and per jacket is the same for both shipments.
10s + 20j = 800
5s + 15j = 550
s = sweaters
j = jackets
What is the cost of one jacket?
*
1 point
$20
$30
$40
$110
To find the cost of one jacket, we need to solve the system of equations:
10s + 20j = 800
5s + 15j = 550
We can simplify the equations by dividing both sides of each equation by their respective coefficients:
s + 2j = 80
s + 3j = 110
Now, we can subtract the first equation from the second equation to eliminate the s term:
(s + 3j) - (s + 2j) = 110 - 80
j = 30
Therefore, the cost of one jacket is $30.