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

Hint: 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.