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Answer 1 · 2016-09-11T16:38:42

$7+21+39 = 67 " inches"$

All the lengths are described in terms of the first piece, so let's define that as the variable.

Let the length of the first piece be $x$

1st piece: $x$
2nd piece: $3x$
3rd piece: $5x +4$

All 3 pieces together make 67 inches, write an equation to show this

$x+3x+5x+4 = 67$

$9x +4 = 67$

$9x +4 - 4 = 67 - 4$

$9x = 63$

$x = 7$

Go back to the original definitions of the lengths:

1st piece: $x = 7 " inches"$
2nd piece: $3x = 3xx 7 = 21 " inches"$
3rd piece: $5x +4 = 5xx7+4 = 39 "inches"$

Check: $7+21+39 = 67 " inches"$