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

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%.

Answer by mananth(16946)   (Show Source): 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

[(9x/10)*100] =160*112.5
9x/10 = 160 *112.5 / 100
9x= 10* 160*112.5 / 100
x= 10*160*112.5/100* 9

x=200
This will be the marked price $200
Answer by richwmiller(17219)   (Show Source): You can put this solution on YOUR website!
160*1.125=d
.9m=d
d=180 discounted price
m=200 marked price
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