# Question #aab2d

Sep 11, 2016

$7 + 21 + 39 = 67 \text{ inches}$

#### Explanation:

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: $3 x$
3rd piece: $5 x + 4$

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

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

$9 x + 4 = 67$

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

$9 x = 63$

$x = 7$

Go back to the original definitions of the lengths:

1st piece: $x = 7 \text{ inches}$
2nd piece: $3 x = 3 \times 7 = 21 \text{ inches}$
3rd piece: $5 x + 4 = 5 \times 7 + 4 = 39 \text{inches}$

Check: $7 + 21 + 39 = 67 \text{ inches}$