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Question 1097762: A trader made a profit of 50% on merchandise that he sold for R10000 calculate the original total price of the goods
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! he sells it for 10,000.
his percent profit is 50%.
profit equals selling price minus cost.
profit rate equals profit / cost.
profit percent equals profit rate * 100%.
let c represent his cost.
let s represent his selling price.
let p represent his profit.
the equation for profit is p = s - c.
you know his selling price is 10,000, so the equation becomes p = 10,000 - c.
profit rate is equal to p / c.
since p = 10,000 - c, then the equation for profit rate becomes p = (10,000 - c) / c
since profit percent = 50%, then profit rate = 50% / 100% = .5.
the equation of p = (10,000 - c) / c becomes .5 = (10,000 - c) / c
multiply both sides of this equation by c to get .5 * c = 10,000 - c.
add c to both sides of this equation to get 1.5 * c = 10,000.
divide both sides of this equation by 1.5 to get c = 10,000 / 1.5.
solve for c to get c = 6666.67 rounded to two decimal places.
that's the cost.
possibly a simpler way of looking at this would be:
x is the cost.
profit is 50% of the cost which is equal to .5 * x.
x + .5 * x = 10,000
this results in 1.5 * x = 10,000.
solve for x to get x = 10,000 / x = 6666.67 rounded to two decimal places.
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