Question

If $S$ is the sum of $8,6,4,2{\text{ and x,}}$ what must be the value of ${\text{x}}$ for ${\text{x}}$ to equal $\dfrac{1}{5}S$ ?
A. $4$
B. $5$
C. $6$
D. $3$

Answer 1

To solve the given question we write $S$ as sum of the given numbers $8,6,4,2{\text{ and x}}$ then substitute the value of $x$ as given in question as $\dfrac{1}{5}S$ .Then we find value of $S$, then find $x$ using $x = \dfrac{1}{5}S$.

Complete step by step answer:
First we write S as $S = 8 + 6 + 4 + 2 + x$............(as it was given in question)
But they also gave $x = \dfrac{1}{5}S$
Now substituting value of x in the above equation we as follows
$S = 8 + 6 + 4 + 2 + \dfrac{1}{5}S$
Now taking $\dfrac{1}{5}S$ on to L.H.S we get
$\Rightarrow S - \dfrac{1}{5}S = 8 + 6 + 4 + 2$
$\Rightarrow \dfrac{4}{5}S = 8 + 6 + 4 + 2$
$\Rightarrow S = \dfrac{{20 \times 5}}{4}$
$\Rightarrow S = 25$
Using mathematical operations we found the value of S from the equation as $25$ .
Now we find the value of x using $x = \dfrac{1}{5}S$
Substitute the value of S and we get as follows
$x = \dfrac{1}{5} \times 25$
$\therefore x = 5$
Therefore the value of x is 5.

Hence, the correct answer is option ${\text{B}}$.

Note: In order to solve this type of problems the key is to substitute the unknown value in the equation in such a way that they help in simplification of the given relation. This problem can also be solved by directly verifying the options, taking the value of x and then doing all the mathematical operations results in finding the value of S .Then if S is 5 times the value x, then the option which will be correct is B.