Puzzle 62 - Legacy

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 A man left legacies to his 3 sons and a hospital. The total amount of his legacy was $1320. If he had left the hospital legacy to his first son, he would have received as much as other two sons together. If he had left the hospital legacy to his second son, he would have received twice as much as the other two sons together. If he had left the hospital legacy to his third son, he would have received thrice as much as the other two sons together.

Find the amount of each legacy. 

Solution:

Let the legacies of first, second and third sons be x,y and z respectively. Let h be the legacy of the hospital.

Given

x+y+z+h = 1320
x+h = y+z
y+h = 2* (x+z)
z+h = 3*(x+y)

Replacing h with 1320-x-y-z, we get the equations as

x+1320-x-y-z = y+z
y+1320-x-y-z = 2*(x+z)
z+1320-x-y-z = 3*(x+y)

Simplifying and solving we get

x = 55, y = 275 and z = 385. And h = 605

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