SOLUTION: Greetings! I need help on this problem which, albeit it looks terribly simple in a first glance, I'm finding difficulty in getting the right solution. the answer to this problem is
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Question 282751: Greetings! I need help on this problem which, albeit it looks terribly simple in a first glance, I'm finding difficulty in getting the right solution. the answer to this problem is supposed to be $200. Here goes:
A dealer bought a phonograph for $160. For how many dollars must he mark it so that after deducting 10% of the marked price, he may sell it at a profit of 12-1/2% of the cost?
Thanks very much for the help guys! :) Found 3 solutions by Theo, mananth, richwmiller:Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website! C = Cost of Phonograph = $200.
M = Marked Up Price of Phonograph = (1+x) * C.
D = Discounted Selling Price of Phonograph = 1.125 * C.
D = Discounted Selling Price of Phonograph = .9 * M.
Note that M - .1 * M = .9 * M.
You have 2 equations that need to be solved simultaneously.
They are:
D = 1.125 * C and D = .9 * M.
Since M = (1+x) * C, Then the equations become:
D = 1.125 * C and D = .9 * (1+x) * C.
Since both expressions equal to D, then both expressions are equal to each other and you get:
1.125 * C = .9 * (1+x) * C
Divide C from both sides of this equation to get
1.125 = .9 * (1+x)
Divide both sides of this equation by .9 and you get:
1.25 = 1 + x
Subtract 1 from both sides of this equation and you get
.25 = x
That's your answer.
The Price needs to be marked up 25% in order to sell it at a discount of 10% and still make a profit of 12.5%
In numbers, this is what happens:
The cost is $200.
the marked price is 1.25 * 200 = $250.
The discounted price is $250 - .1 * $250 = $250 - $25 = $225.
The profit is $225 - $200 = $25.
The profit margin is $25/$200 = .125 = 12.5%.
You can put this solution on YOUR website! There are many methods to solve this problem.
let the marked price be x
he wants to give discount of 10%
So his sale price will be x-x/10
when the sale price is 112.5 the cost price will be 100 (12.5 % he wants to add profit)
when the sale price is (x-x/10) the cost price will be
(x-x/10) *100 / 112.5 = 160 ( cost price)
[(10x-x /10)* 100] / 112.5 =160
