Question 316496
Let G be the amount of gold, C copper, T tin, I iron.
1.{{{G+C+T+I=60}}}
2.{{{G+C=(2/3)(60)=40}}}
3.{{{G+T=(3/4)(60)=45}}}
4.{{{G+I=(3/5)(60)=36}}}
From eq. 2,
{{{C=40-G}}}
From eq. 3,
{{{T=45-G}}}
From eq. 4,
{{{I=36-G}}}
Now substitute all of those expressions into eq. 1 to solve for G.
{{{G+(40-G)+(45-G)+(36-G)=60}}}
{{{-2G+121=60}}}
{{{-2G=-61}}}
{{{highlight( G=61/2)}}}
Now go back to each equation to solve for the other variables,
{{{C=80/2-61/2}}}
{{{highlight( C=19/2)}}}
{{{T=90/2-61/2}}}
{{{highlight( T=29/2)}}}
{{{I=72/2-61/2}}}
{{{highlight( I=11/2)}}}