Question 771029
Let the first piece (longest) of ribbon to be x, the second piece (shortest) of ribbon to be y while the third piece of ribbon to be z.
{{{x+y+z=81}}} --> Equation 1
{{{x=y+34}}} --> Equation 2 ... Substitute {{{x=y+34}}} into Equation 3
{{{z=x/2}}} --> Equation 3
{{{z=(y+34)/2}}}
Substitute {{{x=y+34}}} and {{{z=(y+34)/2}}} into Equation 1.
{{{(y+34)+y+((y+34)/2)=81}}}
{{{y+34+y+(y+34)/2=81}}}
{{{2y+68+2y+y+34=162}}}
{{{2y+2y+y=162-68-34}}}
{{{5y=60}}}
{{{y=60/5}}}
{{{y=12}}}
Substitute {{{y=12}}} into Equation 2.
{{{x=12+34}}}
{{{x=46}}}
Substitute {{{x=46}}} into Equation 3.
{{{z=46/2}}}
{{{z=23}}}
Therefore, the longest ribbon, x = 46 inches, the shortest ribbon, y = 12 inches and the third piece of ribbon, z = 23 inches.