SOLUTION: A man left legacies to his three sons and to a hospital, amounting in all to $1,320.00. If he had left the hospital legacy also to his first son, that son would have received as mu

Question 809064: A man left legacies to his three sons and to a hospital, amounting in all to $1,320.00. If he had left the hospital legacy also to his first son, that son would have received as much as the other two sons together. If he had left it 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 then thrice as much as the first son and second son together. Find the amount of each legacy.
Found 2 solutions by richwmiller, stanbon:
Answer by richwmiller(17219) (Show Source): You can put this solution on YOUR website!
asked two minutes ago
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
A man left legacies to his three sons and to a hospital, amounting in all to $1,320.00. If he had left the hospital legacy also to his first son, that son would have received as much as the other two sons together. If he had left it 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 then thrice as much as the first son and second son together. Find the amount of each legacy.
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Equations:
a + b + c + h = 1320
a+h = b+c
b+h = 2(a+c)
c+h = 3(a+b)
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Rearrange:
a + b + c + h = 1320
a - b - c + h = 0
2a- b +2c - h = 0
3a+3b -c - h = 0
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I used my TI-84 to get:
a = 55
b = 275
c = 385
h = 605
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Cheers,
Stan H.
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