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Question

An art dealer sold two artworks for $1520 thereby making a profite of 25% on the first work and 10% profit of the other, where as if he had approached any exhibition he would have sold them together for $1535 with a profit of 10% on the first and 25% on the other artwork. Find the actual cost of each artwork.

Answer 1

The first is 600 and the second is 700.

(If you sell something for 25% profit it means you sold it for 25% more than its worth, making the selling price 125% of the actual cost, or 1.25 x actual cost.)

Set up 2 equations:
1.25a + 1.10b = 1520
1.10a + 1.25b = 1535
solve for a in first equation:
a = (1520-1.10b)/1.25
put this value for a in the second equation:
1.10(1520-1.10b)/1.25 + 1.25b = 1535
solve for b to get
b=700
put this value in either equation to get:
a=600

Answer 2

Call the artowrks A and B.

First case,
1.25*A + 1.1*B = 1520 or 5/4 A + 11/10 B = 1520
Second case
1.1*A + 1.25*B = 1535 or 11/10A + 5/4 B =　1535

make a shortcut, as the 2 cases are only different by $15

1.25A + 1.1B + 15 = 1.1A +1.25B
or in fraction form
5/4A + 11/10B + 15 = 11/10A + 5/4B

change everything into 1/20ths to make it easier

25/20A + 22/20B + 15 = 22/20A + 25/20B
simplify
3/20A + 15 = 3/20B
change 15 into 1/20ths
3/20A + 300/20 = 3/20B
can get rid of 1/20ths
3A + 300 = 3B
divide by 3
A + 100 = B
substitute back into case 1

5/4 A + 11/10(A + 100) = 1520
25/20 A + 22/20(A + 100) = 1520
47/20 A + 2200/20 = 1520
47/20A + 110 = 1520
47/20A = 1410
47A = 20 * 1410
A = 28200/47

A = 600 so B = 700

Answer 3

Let the cost of 1st work be (in dollars) x and of the second y.
It is given that the profit on the first transaction is 25% and 10% yielding in all 1520. Hence 1.25x+1.1y=1520.
Similarly, from the exhibition transaction, the equation would be
1.1x+1.25y=1535.
Multiplying first equation by 1.1 and the second by 1.25, we get
1.375x+1.21y=1672
1.375x+1.5625=1918.75.
Subtracting the first equation from the second,
0.3525y=246.75, giving y=700. Substituting this value for y in the original first equation, 1.25x+770=1520, and so x=600.
Hence x=$ 600, y=$ 700.

Answer 4

Let A and B be the costs of the two pieces of art. If there was a 25% profit on the first work, then it sold for a total of the original price plus 25% of it. Similarly, the second piece sold for its actual cost plus 10% of that. The two sales prices add up to 1520. So:

(A + 0.25A) + (B + 0.10B) = 1520

Use the rest of the words and the same approach to get the second equation:

(A + 0.10A) + (B + 0.25B) = 1535

1.25A + 1.1B = 1520
1.1A + 1.25B = 1535

You've got 2 equations with 2 unknowns, which you can now solve (Hint: multiply both sides by 100 to get rid of the decimal, which might make it less messy to work with).

Answer 5

first work $600
second $700