Question 165788
Let's name everyone's cut length after the first letter of their name.
All their lengths together equal 30.
1.{{{I+Z+D+E=30}}}
"Denys wants twice as much as Ivan does"
2.{{{D=2*I}}}
"Zoe wants twice as much as Denys does"
3.{{{Z=2*D=2*(2*I)=4*I}}}
"Zoe wants half as much as Ethan does" 
4.{{{Z=(1/2)E}}}
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Since 3 and 4 both equal Z, set them equal to each other,
{{{4*I=(1/2)E}}}
5.{{{E=8*I}}}
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Now you can form an equation with only "I" as the variable, using substitutions from equations 2,3,and 5.
1.{{{I+Z+D+E=30}}}
{{{I+(4*I)+(2*I)+(8*I)=30}}}
{{{15*I=30}}}
{{{I=2}}}
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Now go back and substitute this value in each of the equations,
2.{{{D=2*I=2(2)=4}}}
3.{{{Z=4*I=4(2)=8}}}
5.{{{E=8*I=8(2)=16}}}
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Ivan gets 2 feet, Zoe gets 8 feet, Denys gets 4 feet and Ethan gets 16 feet.