Question 80797
Let the cost of the first art work = $x
Profit = 25% = 0.25
So sale price = x + 0.25x
              = 1.25x
Let the cost of the second art work = $y
Profit = 10% = 0.10
So sale price = y + 0.10y
              = 1.10y

Total sale price given = $1520

==> 1.25x + 1.10y = 1520 ------------(1)

Case (ii)

Profit on first work = 0.10
so sale price = 1.10x

Profit on second work = 0.25
so sale price = 1.25y 

Total sale price given = $1535

==> 1.10x + 1.25y = 1535 ------------(2)

Adding 1 and 2 we get, 2.35x + 2.35y = 3050

==>                       x + y = 1300 [dividing by 2.35 throughout]------(3)

Subtracting 1 and 2 we get, 0.15x - 0.15y = - 15

==>                       x - y = -100 [dividing by 0.15 throughout]------(4)

Adding 3 and 4,  2x = 1200
==>               x = 600

plugging in (3), we get y = 700

Thus the art works cost $600 and $ 700 respectively.