Suzy's $5 \mathrm{~m}$ long ribbon has shaded and unshaded sections of equal length, as shown. Points $A, B, C, D, E$ are equally spaced along the ribbon.

![](https://cdn.mathpix.com/cropped/2024_04_20_46ead6524a8d61e21c51g-033.jpg?height=93&width=596&top_left_y=2271&top_left_x=729)

If Suzy wants a ribbon that is $\frac{11}{15}$ of the size of this ribbon, at which point could she make a single vertical cut?
(A) $A$
(B) $B$
(C) $C$
(D) $D$
(E) $E$

Grade 7
The shaded and unshaded sections of the ribbon have equal length.

Since there are 5 such sections, then each shaded and unshaded section has length equal to $\frac{1}{5}$ or $\frac{3}{15}$ of the length of the ribbon.

All measurements which follow are made beginning from the left end of the ribbon.

Point $A$ is located 3 sections from the left end of the ribbon, or at a point $3 \times \frac{3}{15}=\frac{9}{15}$ along the length of the ribbon.

Point $D$ is located 4 sections from the left end of the ribbon, or at a point $4 \times \frac{3}{15}=\frac{12}{15}$ along the length of the ribbon.

All points are equally spaced, and so points $B$ and $C$ divide the unshaded section between points $A$ and $D$ into 3 equal lengths.

Since $A$ is located $\frac{9}{15}$ of the ribbon length from the left end, and $D$ is located $\frac{12}{15}$ of the ribbon length from the left end, then $B$ is located at $\frac{10}{15}$ of the ribbon length, and $C$ is located at $\frac{11}{15}$ of the ribbon length.

Thus, if Suzy makes a vertical cut at point $C$, the portion of the ribbon to the left of $C$ will be $\frac{11}{15}$ of the size of the original ribbon.

We note that no point is located more than 2 sections from the right end of the ribbon.

That is, no point is located more than $2 \times \frac{3}{15}=\frac{6}{15}$ along the length of the ribbon when measured from the right end, and so measurements are taken from the left end of the ribbon.

ANSWER: (C)