SOLUTION: If something was purchased at $X, and sold for $28, making X% profit, what was the cost of that something? Not certain, but does it have something to do with X^2?

Question 1043579: If something was purchased at $X, and sold for $28, making X% profit, what was the cost of that something?
Not certain, but does it have something to do with X^2?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
the cost was x dollars.
the item was sold for 28 dollars.
the profit was x%.

profit = revenue minus cost.

therefore profit = 28 - x.

this profit equals x % of the cost.

x % of the cost is equal to x / 100 * the cost.

since the cost is x, then x % of x is equal to x / 100 * x which is equal to x^2 / 100.

this means that the profit is equal to x^2 / 100.

since the profit is also equal to 28 - x, you get:

x^2 / 100 = 28 - x

multiply both sides of this equation by 100 to get:

x^2 = 2800 - 100 * x

add 100 * x and subtract 2800 from both sides of this equation to get:

x^2 + 100 * x - 2800 = 0

use the quadratic formula to solve for x.

you get:

x = -122.80109889 or x = 22.80109889

since x represents the cost, and since the cost can't be negative, you are left with:

x = 22.80109889

that's your cost.

x % would be equal to 22.80109889 %

profit = revenue - cost.

profit = 28 - 22.80109889 = 5.198901107

percent profit = 5.198901107 / 22.80109889 = .2280109889 * 100 = 22.80109889 %.

your solution is that x = 22.80109889 and x % = 22.80109889 %.

you are correct.

the solution does have something to do with x^2.

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