SOLUTION: Make a crown of gold, copper, tin, and iron weighing 60 minae: gold and copper shall be two-thirds of it; gold and tin three-fourths of it; and gold and iron three-fifths of it:

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Question 316496: Make a crown of gold, copper, tin, and iron weighing 60 minae: gold and copper shall be two-thirds of it; gold and tin three-fourths of it; and gold and iron three-fifths of it: Find the weights of gold, copper, tin and iron required.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Let G be the amount of gold, C copper, T tin, I iron.
1.G%2BC%2BT%2BI=60
2.G%2BC=%282%2F3%29%2860%29=40
3.G%2BT=%283%2F4%29%2860%29=45
4.G%2BI=%283%2F5%29%2860%29=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%2B%2840-G%29%2B%2845-G%29%2B%2836-G%29=60
-2G%2B121=60
-2G=-61
highlight%28+G=61%2F2%29
Now go back to each equation to solve for the other variables,
C=80%2F2-61%2F2
highlight%28+C=19%2F2%29
T=90%2F2-61%2F2
highlight%28+T=29%2F2%29
I=72%2F2-61%2F2
highlight%28+I=11%2F2%29