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?
Suppose Julie has j dollars.
The price of a t-shirt is t dollars
The price of a hat is h dollars
8t = j + 28
4t + 3h = j - 17
h=5, so,
8t - j = 28
4t -j = -32
4t = 60
t = 15
j = 92
So, Julie has $92
8 T-shirts cost $120, so she's $28 short
4 T's + 3 hats = $75, so she has $17 extra
Well, it seems like Julie's T-shirt shopping spree led to some money troubles! Let's do some math and figure out how much money she had in the beginning.
If Julie bought 8 T-shirts and ended up being short $28, we can assume that each T-shirt costs the same amount. Let's call the cost of each T-shirt "X." So, we have 8X - 28 = 0.
Now, if she bought 4 T-shirts and 3 baseball hats and had $17 left, we can assume that each T-shirt and hat together cost the same total amount. Each hat costs $5, so let's call the cost of each T-shirt and hat paired together "Y." We have 4X + 3 * 5 = Y + 17.
Now, we have two equations:
1) 8X - 28 = 0
2) 4X + 3 * 5 = Y + 17
Solving these equations will give us the values of X and Y, which in turn will give us the amount of money Julie had in the beginning. However, since I'm not given the specific values of X and Y, I cannot determine the exact amount of money Julie had. But hey, at least this math problem gave us some good brain exercise, didn't it?
Let's analyze the information given step by step.
Let's assume the cost of each T-shirt is "x" dollars.
According to the first condition, if Julie bought 8 T-shirts, she would be short $28. This can be represented by the equation:
8x - $28 = $0 (1)
According to the second condition, if Julie bought 4 T-shirts and 3 baseball hats, she would have $17 left. Each hat costs $5, so the total cost of the 3 hats is $5 × 3 = $15. This can be represented by the equation:
4x + $15 - $17 = $0 (2)
We can solve these two equations simultaneously to find the value of "x" and then determine the initial amount of money Julie had.
Let's solve equations (1) and (2):
8x - $28 = $0
4x + $15 - $17 = $0
Rearranging equation (1):
8x = $28
x = $28 ÷ 8
x = $3.5
Substituting the value of "x" into equation (2):
4($3.5) + $15 - $17 = $0
$14 + $15 - $17 = $0
$29 - $17 = $0
$12 = $0
This is not possible according to arithmetic. It means there is no solution that satisfies both conditions.
Therefore, there is an inconsistency in the information provided.
To solve the problem, we need to set up equations based on the given information.
Let's assign a variable to represent the cost of each T-shirt and the total amount of money Julie had in the beginning.
Let's say the cost of each T-shirt is 'x' dollars.
According to the first condition, if Julie bought 8 T-shirts, she would be short $28. This can be written as:
8x = x - 28
Simplifying the equation, we get:
8x - x = -28
7x = -28
Dividing both sides of the equation by 7, we find:
x = -4
So the cost of each T-shirt is $-4 (which means Julie received some kind of discount).
Now, let's calculate the total amount of money Julie had in the beginning by substituting this value into the equation:
Total money = 8x = 8 * (-4) = -32
So, Julie had $-32 in the beginning.