at the local clothing store, 3 similar shirts and 4 similar jackets cost $360 and 1 shirt and 3 jackets cost $220. find the cost of each shirt.
3s + 4j= 360
s + 3j = 220
from the second: s = 220 - 3j
sub into the first:
3(220 - 3j) + 4j = 360
-5j = -300
j = 60
then s = 220 - 180 = 40
650-40=510
Let's assume the cost of each shirt is S and the cost of each jacket is J.
According to the given information, we have the following equations:
3S + 4J = 360 (Equation 1)
S + 3J = 220 (Equation 2)
To solve the system of equations, we can use the method of substitution or elimination.
Let's use the method of substitution. We rearrange Equation 2 to solve for S:
S = 220 - 3J (Equation 3)
Now, substitute Equation 3 into Equation 1:
3(220 - 3J) + 4J = 360
Distribute the 3:
660 - 9J + 4J = 360
Combine like terms:
-5J = 360 - 660
-5J = -300
Divide both sides by -5:
J = -300 / -5
J = 60
Now, substitute the value of J into Equation 3 to find S:
S = 220 - 3(60)
S = 220 - 180
S = 40
Therefore, the cost of each shirt is $40.
To find the cost of each shirt, let's assign variables to the unknowns. Let's call the cost of a shirt "S" and the cost of a jacket "J".
According to the problem, we know that:
- 3 similar shirts and 4 similar jackets cost $360: 3S + 4J = 360 (Equation 1)
- 1 shirt and 3 jackets cost $220: S + 3J = 220 (Equation 2)
To solve this system of equations, we can use the method of substitution or elimination. Let's use the elimination method.
Multiply Equation 2 by 3 to make the coefficients of J the same in both equations:
3(S + 3J) = 3S + 9J = 3 * 220 = 660
Now, let's subtract Equation 1 from the new equation we obtained:
(3S + 9J) - (3S + 4J) = 660 - 360
3S + 9J - 3S - 4J = 300
This simplifies to:
5J = 300
Now, we can solve for J by dividing both sides of the equation by 5:
J = 300 / 5
J = 60
We have found that the cost of a jacket is $60. Now, we can substitute this value back into Equation 2 to find the cost of a shirt:
S + 3J = 220
S + 3(60) = 220
S + 180 = 220
S = 220 - 180
S = 40
Therefore, the cost of each shirt is $40.