3 shirts and 2 hats cost $52. 2 shirts and 1 hat cost $32. Find the cost of each.
To solve this problem, we can assign variables to the unknown quantities, namely the cost of a shirt and the cost of a hat. Let's call the cost of a shirt "x" and the cost of a hat "y".
From the information given, we can form two equations as follows:
Equation 1: 3x + 2y = 52 (since 3 shirts and 2 hats cost $52)
Equation 2: 2x + y = 32 (since 2 shirts and 1 hat cost $32)
Now, we can solve this system of equations. There are several ways to do this, but let's use the substitution method.
Step 1: Solve Equation 2 for y in terms of x:
y = 32 - 2x
Step 2: Substitute the expression for y in Equation 1:
3x + 2(32 - 2x) = 52
Step 3: Simplify and solve for x:
3x + 64 - 4x = 52
-x + 64 = 52
-x = 52 - 64
-x = -12
x = -12/-1
x = 12
Step 4: Substitute the value of x back into Equation 2 to find y:
2(12) + y = 32
24 + y = 32
y = 32 - 24
y = 8
Therefore, the cost of each shirt is $12 and the cost of each hat is $8.
3s + 2h = 52
2s + h = 32
h = 32 - 2s
3s + 2(32 - 2s) = 52
3s + 64 - 4s = 52
12 = s
One shirt costs $12. How much does a hat cost?