La purchased a case of shirts for$450.00, kept 2 shirts for himself, sold rest for $560.00, profit of $10 on each. how many shirts were in the case?
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Let the number of shirts he bought is x with a cost of C for each shirt.
==> Total cost = cost per shirt *number of shirts.
==> 450 = C*x ...........(1)
Now he kept 2 shirts and sold the rest.
Then, the number of shirts he sold is (x-2).
He sold each shirt with a profit of $10. Then, the selling price = (C+10).
==> Total selling price = (x-2)*(C+10) = 560
==> 560 = (x-2)(C+10)
==> 560 = C*x + 10x - 2C -20
==> 580 = C*x + 10x -2C
But we know that C*x = 450
==> 580 = 450 + 10x - 2c
==> 130 = 10x -2C
Divide by 2.
==> 65 = 5x -C
==> C = 5x-65
Now substitute in (1).
==> C*x = 450
==> (5x-65)x = 450
==> 5x^2 - 65x -450 = 0
Divide by 5:
==> x^2 -13x -90 = 0
==> (x-18)(x+5) = 0
==> x = 18
==> x= -5 ( Not valid)
Then, the number of shirts were in the case is 18 shirts.
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