Question 282751
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%.