If Julie bought 8 T-shirts, she would be short $28. If she bought 4 T-shirts and 3 baseball hats, she would have $17 left. If each hat cost $5, how much money did she have in the beginning?
To solve this problem, we can use a system of equations. Let's define "x" as the cost of each T-shirt and "y" as the amount of money Julie had in the beginning.
According to the problem statement, if Julie bought 8 T-shirts, she would be short $28. This can be written as:
8x = y - 28 (Equation 1)
Similarly, if she bought 4 T-shirts and 3 baseball hats, she would have $17 left. Let's calculate the cost of 4 T-shirts and 3 hats. Each T-shirt costs "x" and each hat costs $5. So, the cost of 4 T-shirts and 3 hats would be:
4x + 3*5 = y - 17
4x + 15 = y - 17
4x = y - 32 (Equation 2)
Now, we have a system of equations:
8x = y - 28 (Equation 1)
4x = y - 32 (Equation 2)
To find the value of "y," we can solve this system of equations. Subtracting Equation 2 from Equation 1, we get:
8x - 4x = (y - 28) - (y - 32)
4x = 32 - 28
4x = 4
Dividing both sides of the equation by 4, we find:
x = 1
Now, substituting the value of "x" back into Equation 1, we have:
8 * 1 = y - 28
8 = y - 28
Adding 28 to both sides of the equation, we find:
y = 8 + 28
y = 36
Therefore, Julie had $36 in the beginning.