a wholesaler bought a batch of t-shirts for $77.00.She gave two of the T-shirts to her daughters and then sold the rest for a total of $90.If the wholesaler sold each T-shirt for $2 more than it cost her,how much did she pay for each T-shirt?
Let the number of t-shirts be x.
Cost of each shirt = 77/x.
No of t-shirt sold = x-2.
Selling price of each t-shirt = 90/(x-2)
By the problem,
90/(x-2) - 77/x = 2
or, (90x - 77x + 154)/x^2-2x = 2
or, 2x^2 - 17x - 154 = 0
or, 2x^2 - 28x + 11x -154 = 0
or, (2x+11)(x-14) = 0
or, x = -11/2 or 14
as the cost can't be negative, the cost of each t-shirt = $14.
cost of each tshirt is 77/14=$5.5
To find out how much the wholesaler paid for each T-shirt, let's break down the information given:
1. The wholesaler bought a batch of t-shirts for $77.00.
2. She gave two t-shirts to her daughters, which means she sold (total t-shirts - 2) t-shirts.
3. She sold the remaining t-shirts for a total of $90.
4. The price at which she sold each t-shirt was $2 more than what it cost her.
Now, let's determine the number of t-shirts she sold. We know that she gave two t-shirts to her daughters, so the number of t-shirts sold can be calculated as (total t-shirts - 2).
Let's assign a variable to represent the number of t-shirts bought, say 'x'. Since 'x' represents the total t-shirts bought, the number of t-shirts sold would be (x - 2).
We can also assign another variable to represent the cost of each t-shirt, say 'y'. The selling price for each t-shirt would then be (y + 2) (because she sold each t-shirt for $2 more than it cost her).
From the given information, we can form the following equation:
(x - 2) * (y + 2) = $90
Now, we can solve this equation to find the values of 'x' and 'y'.
(x - 2) * (y + 2) = $90
Expanding the equation:
xy + 2x - 2y - 4 = $90
Rearranging the terms:
xy + 2x - 2y = $90 + 4
xy + 2x - 2y = $94
We are given that the wholesaler bought the batch of t-shirts for $77, so we have another equation:
xy = $77
Now, we can substitute the value of 'xy' from the second equation into the first equation:
$77 + 2x - 2y = $94
2x - 2y = $94 - $77
2x - 2y = $17
Dividing both sides of the equation by 2:
x - y = $8.50
Now, let's solve this equation to find the value of 'x':
x - y = $8.50
Since we do not have the value of 'y', we cannot solve for the exact cost of each t-shirt. However, from the information given, we know that the wholesaler sold each t-shirt for $2 more than it cost her. So, we can assume that the cost of each t-shirt is $8.50 - $2, which equals $6.50.