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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hala718 | High School Teacher | (Level 1) Educator Emeritus

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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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