Question

What percent of 84 is 14?

Answer 1

Hint: We are given a number 14 and we are asked to find that what percent of 84 is this number. We will first let that the given percent be \[x\%\]. So, we have the expression as \[x\%\] of 84 is 14, that is, \[x\%\times 84=14\]. We will open up this expression and write this expression in terms of ‘x’ and then solve it further to find the value of ‘x’. Hence, we will have the required value of the percent of 84 which gives the values as 14.

Complete step-by-step solution:
According to the given question, we are given a number 14 and we are asked in the question to find the percent of 84 which gives us the value as 14.
Firstly,
We will let the percent be \[x\%\]
Then, based on the given values, we will write the appropriate expression.
So, we have the expression as \[x\%\] of 84 is 14, that is,
\[\Rightarrow \dfrac{x}{100}\times 84=14\]
So, now, we will write the above expression in terms of ‘x’ and solve it further, and we get,
We will cross multiply the 100 over to the other side and we get,
\[\Rightarrow 84x=1400\]
Writing the above expression in terms of ‘x’, we get,
\[\Rightarrow x=\dfrac{1400}{84}\]
We will now be simplifying the above ration and we get,
\[\Rightarrow x=\dfrac{700}{42}\]
Now, dividing the numerator and denominator by 14, we get,
\[\Rightarrow x=\dfrac{50}{3}\]
Or
\[\Rightarrow x=16.66\]
Therefore, the percent of 84 that gives 14 is \[\dfrac{50}{3}\%\] or \[16.66\%\].

Note: The expression should be made correctly, do not intermix the values and make it something like the expression as follows, \[x\%\times 14=84\]. This is incorrect as this expression states, x percent of 14 is 84, but the question was other way round. So, make sure this doesn’t happen. Also, while writing the expression in terms of ‘x’ do it step wise to prevent any mistakes while cross multiplying or simplifying the ratio.