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musicgold

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Hi,

This is not homework. I am struggling with a puzzle from this

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.

## a+b+c+h =1320 ~ ....(1)\\

h= b+c-a ~ ....(2)\\

h=2a +2c-b ~ ....(3)\\

h=3a+3b-c ~ ....(4)##

Using equation (1), I got ## c =660 -b##

Also I equated equations (2) and (3) to get ## 2b = 3a +c##

I substituted the value of c in this equation to get ##b =220 +a##

Using these values of c and b in equation (1) I got ##b+h=880##

I am not sure what to do after this.

Also, is there an elegant way to solve this problem?

Thanks

This is not homework. I am struggling with a puzzle from this

__book (__page 6, puzzle #13). I know the answer of the puzzle but I can't seem to figure out a good approach.

1. Homework Statement1. Homework Statement

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.

## Homework Equations

## a+b+c+h =1320 ~ ....(1)\\

h= b+c-a ~ ....(2)\\

h=2a +2c-b ~ ....(3)\\

h=3a+3b-c ~ ....(4)##

## The Attempt at a Solution

Using equation (1), I got ## c =660 -b##

Also I equated equations (2) and (3) to get ## 2b = 3a +c##

I substituted the value of c in this equation to get ##b =220 +a##

Using these values of c and b in equation (1) I got ##b+h=880##

I am not sure what to do after this.

Also, is there an elegant way to solve this problem?

Thanks

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