Simultaneous Equations

If 2 rabbits and 4 dogs cost $ 1750, three dogs and 2 cats cost $ 1725 and one cat and 3 rabbits cost $ 675. Find the price of each.
Let cost of 1 rabbit = R, cost of 1 dog = D, cost of 1 cat = C



Conditions

2R + 4D = 1750

D = ( 875 - R)/2   ------------(1)

3D + 2C = 1725  -----------(2)

C + 3R = 675

or, C = 675 - 3R  -----------(3)

Substituting (1) and (3) in (2)

3(875 - R)/2 + 2(675 - 3R) =1725


or -3R - 12R = 1725 x 2 -4 x 675 - 3 x 875

or 15R = 1875

or R = 125

therefore C = 675 - 3R = 300

and D = 375

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