Question
Answers

If one-eight of a pencil is black, half of the remaining is yellow, and the remaining
$3\dfrac{1}{2}$ cm is blue then what is the total length of the pencil?
A. $6$ cm
B. $7$ cm
C. $8$ cm
D. $11$ cm

Answer Verified Verified
Hint: In this problem, first we assume that the total length of pencil is $x$ cm. Then we will use the given information. We will get the linear equation in one variable. After solving the linear equation in one variable, we will get the required length of the pencil.

Complete step-by-step answer:
Let us assume that the total length of pencil is $x$ cm. Now it is given that one-eight of the total length of pencil is of black colour. Therefore, we can say that black part of the pencil is one-eight of $x$. That is, black part $ = \dfrac{x}{8}$ cm.
Now the total length of the pencil is $x$ cm and the length of black part is $\dfrac{x}{8}$ cm. So we can say that length of remaining part is $\left( {x - \dfrac{x}{8}} \right) = \dfrac{{8x - x}}{8} = \dfrac{{7x}}{8}$ cm.
Now it is also given that half of the remaining part is of yellow colour. That is, $\dfrac{1}{2}$ of the remaining part is of yellow colour. Therefore, we can say that length of yellow part is $\dfrac{1}{2}\left( {\dfrac{{7x}}{8}} \right) = \dfrac{{7x}}{{16}}$ cm.
Now it is also given that remaining $3\dfrac{1}{2} = \dfrac{7}{2}$ cm is of blue colour but now we have remaining part of pencil is $\dfrac{{7x}}{{16}}$ . So we can say that the length of the remaining blue part is $\dfrac{{7x}}{{16}}$ which is equal to $\dfrac{7}{2}$. That is, $\dfrac{{7x}}{{16}} = \dfrac{7}{2} \Rightarrow x = \dfrac{{16}}{2} \Rightarrow x = 8$
Therefore, the total length of pencil is $8$ cm.
Therefore, option C is true.

Note:When solving these types of problems,make sure to calculate the remaining portion appropriately in accordance with the data given.General form of linear equation in one variable is $ax + b = 0$ where $a,b$ are integers and $x$ is variable.