SOLUTION: a man bought an article for 300. by selling it at a discount of 25% he made a profit of 15% on the cost. find the list price.

Question 834196: a man bought an article for 300. by selling it at a discount of 25% he made a profit of 15% on the cost. find the list price.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
cost is equal to $300.
let x equal the retail price.
the discount price is therefore equal to x - .25 * x which is equal to .75*x.
his revenue is the discount price.
profit is equal to revenue minus cost.
profit is also equal to 15% of the cost.
15% of 300 is equal to 45 dollar.
profit is equal to 45
revenue is equal to .75x
cost is equal to 300
profit = revenue minus cost becomes:
45 = .75x - 300
add 300 to both sides of this equation to get:
.75x = 345
divide both sides of this equation by .75 to get:
x = 345 / .75 = 460

the original retail price is 460
he sells it as a 25% discount off of the retail price.
the selling price is equal to 460 - .25 * 460 which is equal to 345
he sells it at 345 and his cost is 300 so he makes a profit of 45.
45 / 300 is equal to .15 which is equal to 15% of 300 which is equal to 15% of the cost.

if you let S equal the selling price and you let C equal the cost and you let P = the profit, you will get the equation:
P = S - C
if you let R equal the retail price and you let S equal the retail price minus 25% of the retail price, you will get the equation:
S = R - .25R
if you replace S with R - .25R in the equation of P = S - C, you will get the equation:

P = R - .25R - C

if you let P = .15 * C, then you will get the equation:

.15 * C = R - .25R - C

if you simplify this equation you will get:

.15 * C = .75R - C

if you add C to both sides of this equation, you will get:

.15 * C + C = .75R

if you simplify this equation, you will get:

1.15 * C = .75 * R

if you divide both sides of this equation by .75, you will get:

(1.15 * C) / .75 = R

if you replace C with 300, you will get:

(1.15 * 300) / .75 = R

solve for R and you will get:

R = (1.15 * 300) / .75) = 460.

you can work it either way and you'll come up with the same answer, as you should.

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