Question

Solve for x.
\[3:x::18:6\]

Answer 1

Hint: The sign ‘:’ here is called ‘ratio’ which is roughly the same as division and ‘: :’ is called
‘proportion’. Convert given ratio and proportion format into linear equation and solve them using cross
multiply method.

Complete step-by-step answer:
This is the problem of Chapter Ratio and Proportion. Here, the objective is to find the value of x.
Here for example 4:5 means ‘4 divided by 5’, which is \[\dfrac{4}{5}\].
So, 3:x means ‘3 divided by number x’, so we can write it as \[\dfrac{3}{x}\]
And, 18:6 means ‘18 divided by 6’, so we can write it as \[\dfrac{18}{6}\]
Therefore, we have the whole expression in question which becomes:
\[\dfrac{3}{x}=\dfrac{18}{6}\]
Now, we separate variables and constants and keep one on L.H.S. side and other on R.H.S. side.
We get first after cross multiply:
\[3\times 6=x\times 18\]
Now, keeping variable terms on L.H.S. side and constants term on R.H.S. side. We get:
\[x\times 18=3\times 6\]
\[\Rightarrow 18x=3\times 6\]
\[\Rightarrow 18x=18\]
\[\Rightarrow x=\dfrac{18}{18}\]
\[\Rightarrow x=1\]
So, the found value of x is 1.
Now, we can check whether we solved the above equation correctly or not. For this, we have equation:
\[\dfrac{3}{x}=\dfrac{18}{6}\]
Now, we’ll put the value of x in L.H.S. & check whether L.H.S. is equal to R.H.S. or not.
If L.H.S. = R.H.S. Then, x value is correct
If L.H.S. is not equal to R.H.S. Then, x value is incorrect.
Now,
L.H.S. =\[\dfrac{3}{x}\]
Since, we have got x value as 1 as explained above. Now on putting the value of x in L.H.S. we get:
L.H.S. =\[\dfrac{3}{1}\]
= 3.
So, we found L.H.S. =3.
Now, we have R.H.S. as
=\[\dfrac{18}{6}\]
=3.
Hence, L.H.S. = R.H.S. (Proved).
Therefore, the found value of x as 1 is correct.

Note: First the students should know about the mathematical meaning of ‘:’ & ‘::’. Proportion says two ratios are equal. It can be written in two ways like (1/3) = (2/6) & (a:b) = (c:d). After this, any similar question can easily be solved. Use L.H.S. & R.H.S. to check the correct value of x. If we know the concept, then we can find the answer by using it for competitive exams where time is a factor. Now, 3 and 18 are related to each other in a way. The terms x and 6 must also be related in the same way. On observing, we get that 18 is the sixth multiple of 3, so 6 must also be the sixth multiple of x. Now, according to this, the only possible value of x is 1.