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
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.
To find the cost of one jacket, we can set up a system of equations using the information given.
Let's say the cost of one sweater is S and the cost of one jacket is J.
From the first shipment, we know that there are 20 jackets and the total cost is $800. This can be written as:
20J + 20S = 800
From the second shipment, we know that there are 15 jackets and the total cost is $550. This can be written as:
15J + 5S = 550
Now, we can solve this system of equations to find the values of J and S.
Multiplying the first equation by 3 and the second equation by 4 will make the coefficients of S the same. This gives us:
60J + 60S = 2400
60J + 20S = 2200
Now, subtracting the second equation from the first equation will eliminate J:
(60J + 60S) - (60J + 20S) = 2400 - 2200
40S = 200
S = 200/40
S = 5
Now that we know the cost of one sweater is $5, we can substitute this value back into one of the original equations:
20J + 20S = 800
20J + 20(5) = 800
20J + 100 = 800
20J = 800 - 100
20J = 700
J = 700/20
J = 35
Therefore, the cost of one jacket is $35.
To find the cost of one jacket, we can set up a system of equations based on the information given.
Let's assume the cost of one sweater is "S" and the cost of one jacket is "J".
From the first shipment, we know that there are 20 identical jackets and the total cost was $800. Therefore:
20J + 20S = 800
From the second shipment, we know there are 15 identical jackets and the total cost was $550. Therefore:
15J + 5S = 550
Since the cost per sweater and per jacket are the same for both shipments, we can set up an equation to equate the two costs. This means:
20J + 20S = 15J + 5S
To solve this system of equations, we can use the method of substitution or elimination. Let's use the method of substitution:
From the first equation, we can isolate S:
20J + 20S = 800
20S = 800 - 20J
S = (800 - 20J) / 20
S = 40 - J
Now we substitute this expression for S into the second equation:
15J + 5S = 550
15J + 5(40 - J) = 550
15J + 200 - 5J = 550
10J + 200 = 550
10J = 550 - 200
10J = 350
J = 350 / 10
J = 35
Therefore, the cost of one jacket is $35.