Question 1043579
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.