"an art dealer sold 2 artworks for $1520 thereby making a profit of 25% on the first work and 10% on the other

Question

"an art dealer sold 2 artworks for $1520 thereby making a profit of 25% on the first work and 10% on the other, whreas if he had approached an exhibition he would have sold them together for $1535 with a profit of 10% on thefirst and 25% on the other artwork. Find the actual cost of each artwork.

Answer 1

[1]

Let the actual cost of the artworks be $x and $y respectively.

In the first case,

1.25x+1.10y=1520

or,125x+110y=152000

or,25x+22y=30400...(1)

In the second case,

1.10x+1.25y=1535....(2)

Or,110x+125y=153500

or,22x+25y=30700...(2)

Multiplying(1) by 25 and (2) by 22

625x+550y=760,000

484x+550y=675,400

(subtracting) 141x=84,600

x=600

Plugging x in (2),we get

22*600+25y=30700

13200+25y=30700

25y=30700-13200=17,500

y=700

Therefore,the cost of the first qrtwork is $600 and that of the second one is $700

Answer 2

Let the actual costs be x and y

The statement says that



x*1.25 + y*1.1 = 1520

x*1.1 + y*1.25 = 1535



(x+y)*2.35 = 3055

(y-x)*0.15 = 15



x+y=1300

y-x = 100



So, y = 700 and x = 600

Answer 3

1520 = 1.25A + 1.10B

1535 = 1.10A + 1.25B