Question

The line plot below shows the length of all the pieces of string Jack used. He cut all the pieces from a long string.


If the length of the original string is $7m,$ then what is the remaining length of the string after cutting all the pieces?

• A. $8m$
• B. $5m$
• C. $2m$
• D. $7m$

Answer 1

The correct option is C $2m$

Length of string (m)	Frequency (Number of pieces)	Length of string (m)
$\frac{1}{5}$	$3$	$3\times \frac{1}{5}=\frac{3\times 1}{5}=\frac{3}{5}$
$\frac{2}{5}$	$2$	$2\times \frac{2}{5}=\frac{2\times 2}{5}=\frac{4}{5}$
$\frac{3}{5}$	$1$	$1\times \frac{3}{5}=\frac{1\times 3}{5}=\frac{3}{5}$
$\frac{4}{5}$	$0$	$0\times \frac{4}{5}=\frac{0\times 4}{5}=0$
$1=\frac{5}{5}$	$3$	$3\times \frac{5}{5}=\frac{3\times 5}{5}=\frac{15}{5}$

So, total length of all the string pieces $=\frac{3}{5}+\frac{4}{5}+\frac{3}{5}+\frac{15}{5}=\frac{25}{5}m=5m$

Now, the length of the original string is $7m.$
Therefore, remaining length of the string = original length - total length of all the string pieces
Remaining length of the string $=7m-5m=2m$