SOLUTION: Zuzu sold his dining table set at a loss of 20% .If she had sold it for $800 more , he would have received a profit of 5% .Find the cost price.

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Question 1136508: Zuzu sold his dining table set at a loss of 20% .If she had sold it for $800 more , he would have received a profit of 5% .Find the cost price.
Found 2 solutions by Theo, ikleyn:
Answer by Theo(13342)   (Show Source): You can put this solution on YOUR website!
s is the sale price and c is the cost.

when selling at a 20% loss, s = .8 * c

selling for 800 more gets a 5% profit.

s + 800 = 1.05 * c

in this second equation, replace s with .8 * c to get:

.8 * c + 800 = 1.05 * c

subtract .8 * c from both sides to get 800 = .25 * c

solve for c to get c = 3200

when selling at a 20% loss, s = .8 * 3200 = 2560.

when selling at 800 more than 2560, s = 3360.

profit is (3360 - 3200) / 3200 = 160 / 3200 = .05 = 5%.

the cost price is 3200.


Answer by ikleyn(52776)   (Show Source): You can put this solution on YOUR website!
.

            Let me show you a shorter way to solve the problem and to present the solution. 


Let x be the original cost of the table.


Then Zuzu sold it at the price (1-0.2)*x = 0.8x.


In the second (hypothetical) case Zuzu would sold it at the price (1+0.5)x = 1.05x.


The problem says that


    0.8x + 800 = 1.05x.


Now you solve this equation in ONE LINE


    800 = 1.05x - 0.8x  ====>  800 = 0.25x  ====>  x =  = 3200.    ANSWER

Solved.


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