Question 182379
First off, try to avoid typing in all caps -- it's difficult to read and some folks treat it as shouting.
<br>
Let x = length of 1st piece
Let y = length of 2nd piece
Let z = length of 3rd piece
<br>
We know the total length of the board is 45, so:
<u>Equation 1:</u> {{{ x + y + z = 45 }}}
<br>
We also know that the 2nd piece is 3 times the length of the 1st piece:
<u>Equation 2:</u> {{{ y = 3x }}}
<br>
We also know that he 3rd piece is 5 times the length of the 1st piece:
<u>Equation 3:</u>  {{{ z = 5x }}}
<br>
Now we can substitute the values from equations 2 and 3 into equation 1:
Equation 1:  {{{ x + y + z = 45 }}}
Substitute:  {{{ x + (3x) + (5x) = 45 }}}

Solving for x gives us:
{{{ 9x = 45 }}}
{{{  x = 5 }}}
<br>
Substituting this value back into equations 2 and 3 will give us the values of y and z:
Equation 2: {{{ y = 3x }}}
Substitute: {{{ y = 3(5) }}}
{{{ y = 15 }}}
<br>
Equation 3: {{{ z = 5x }}}
Substitute: {{{ z = 5(5) }}}
{{{ z = 25 }}}
<br>
So the final answers are <b>x = 5</b>, <b>y = 15</b> and <b>z = 25</b>.