Final answer:
To find the cost of one hoodie, a system of equations can be created based on the given information. By solving the system through elimination, it is determined that one hoodie costs $22.
Step-by-step explanation:
Let x represent the cost of one hoodie and let y represent the cost of one hat.
From the given information, we can create the following system of equations:
3x + y = 75
x + 2y = 40
To find the cost of one hoodie, we can solve this system of equations using the method of substitution or elimination. Let's use the elimination method:
By multiplying the second equation by 3, we can eliminate x when we subtract it from the first equation:
3(3x + y) = 3(75)
3x + 6y = 120
3x + y = 75
Subtracting the second equation from the first:
3x + 6y - (3x + y) = 120 - 75
5y = 45
y = 9
Substituting the value of y in one of the original equations, we can find the cost of one hoodie:
x + 2(9) = 40
x + 18 = 40
x = 40 - 18
x = 22
Therefore, one hoodie costs $22.
Learn more about Cost of hoodies and hats