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(52775)   (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.