Four pieces of lumber are placed in parallel positions, as shown, perpendicular to line $M$ :

- Piece $W$ is $5 \mathrm{~m}$ long
- Piece $X$ is $3 \mathrm{~m}$ long and its left end is $3 \mathrm{~m}$ from line $M$
- Piece $Y$ is $5 \mathrm{~m}$ long and is $2 \mathrm{~m}$ from line $M$
- Piece $Z$ is $4 \mathrm{~m}$ long and is $1.5 \mathrm{~m}$ from from line $M$

A single cut, perpendicular to the pieces of lumber,

![](https://cdn.mathpix.com/cropped/2024_04_20_6ed09463f225f8ba1f07g-094.jpg?height=399&width=512&top_left_y=1435&top_left_x=1224)
is made along the dotted line $L$. The total length of lumber on each side of $L$ is the same. What is the length, in metres, of the part of piece $W$ to the left of the cut?
(A) 4.25
(B) 3.5
(C) 3.25
(D) 3.75
(E) 4.0
Suppose that the distance from line $M$ to line $L$ is $d \mathrm{~m}$.

Therefore, the total length of piece $W$ to the left of the cut is $d \mathrm{~m}$.

Since piece $X$ is $3 \mathrm{~m}$ from line $M$, then the length of piece $X$ to the left of $L$ is $(d-3) \mathrm{m}$, because 3 of the $d \mathrm{~m}$ to the left of $L$ are empty.

Similarly, the lengths of pieces $Y$ and $Z$ to the left of line $L$ are $(d-2) \mathrm{m}$ and $(d-1.5) \mathrm{m}$. Therefore, the total length of lumber to the left of line $L$ is

$$
d+(d-3)+(d-2)+(d-1.5)=4 d-6.5 \mathrm{~m}
$$

Since the total length of lumber on each side of the cut is equal, then this total length is $\frac{1}{2}(5+3+5+4)=8.5 \mathrm{~m}$.

(We could instead find the lengths of lumber to the right of line $L$ to be $5-d, 6-d, 7-d$, and $5.5-d$ and equate the sum of these lengths to the sum of the lengths on the left side.)

Therefore, $4 d-6.5=8.5$ or $4 d=15$ or $d=3.75$, so the length of the part of piece $W$ to the left of $L$ is $3.75 \mathrm{~m}$.