SOLUTION: art dealer sold 2 artworks for 1520. made a profit of 25% on the first work and 10% profit on the other. if he had approached any exhibition he would have sold them together for

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Question 41778: art dealer sold 2 artworks for 1520. made a profit of 25% on the first work and 10% profit on the other. 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 find the actual cost each artwork
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Profit = Selling Price - Cost
Let the actual Cost of the paintings together = C
The selling price in the 1st case is $1520
Profit = 1520 - C
Let x = the actual Cost of the 1st painting
Let C - x = the actual Cost of the 2nd painting
Total Profit = Profit from 1st painting + Profit from 2nd painting
1520 - C = .25x + .1(C - x)
The selling price in the 2nd case is $1535
1535 - C = .1x + .25(C - x)
I solved the last equation for C in terms of x
1535 - C = .1x + .25C - .25x
1.25C = 1535 + .15x
C = 1228 + .12x
I substituted this in 1st equation
1520 - 1228 - .12x = .25x + .1(1228 + .12x -x)
292 = .37x + 122.8 + .012x - .1x
292 - 122.8 = .282x
169.2 = .282x
x = 600
C = 1228 + .12x
C = 1228 + 72
C = 1300
C - x = 1300 - 600
C - x = 700
The Cost of each artwork is $600 and $700
check
1520 - C = .25x + .1(C - x)
1520 - 1300 = .25(600) + .1(700)
220 = 150 + 70
220 = 220
OK
1535 - C = .1x + .25(C - x)
1535 - 1300 = .1(600) + .25(700)
235 = 60 + 175
235 = 235
OK