The manager of a discount clothing store received two shipments. The first shipment contains an identical sweaters in 20 identical jackets and cost $800. The second shipment contain five identical sweaters and 15 identical jackets. The cost of a second shipment was $550. the cost per sweater and pro jacket is the same for both shipments. What is the cost of one jacket

Answer 1

Let's assume the cost of one sweater is S and the cost of one jacket is J.
According to the given information, in the first shipment, there are 20 identical jackets and an equal number of identical sweaters. So, the cost of 20 jackets is 20J, and the cost of an equal number of sweaters is 20S. The total cost of the first shipment is $800, so we can write the equation 20J + 20S = 800.

Similarly, in the second shipment, there are 15 identical jackets and 5 identical sweaters. So, the cost of 15 jackets is 15J, and the cost of 5 sweaters is 5S. The total cost of the second shipment is $550, so we can write the equation 15J + 5S = 550.

From these two equations, we can find the values of J and S:

20J + 20S = 800 --> divide both sides by 20 --> J + S = 40 --> equation (1)
15J + 5S = 550 --> divide both sides by 5 --> 3J + S = 110 --> equation (2)

Now, we will solve equations (1) and (2) simultaneously. We can do this by subtracting equation (1) from equation (2):

3J + S - (J + S) = 110 - 40
3J - J + S - S = 70
2J = 70
J = 70/2
J = 35

Therefore, the cost of one jacket is $35.