3
$\begingroup$

'I always exaggerate everything I say by 25%. By how much do I truly exaggerate?'

Hi, I asked myself this question and it is starting to give me a headache. Does anyone have a correct solution? Thanks

$\endgroup$
3
  • $\begingroup$ Do we have to consider that you also exaggerate not all the time, but 75% of the time by x amount? $\endgroup$ – Ryan Oct 22 '19 at 6:56
  • $\begingroup$ Nice, hadn't thought of this. If 'always' is treated as 100% then yes. $\endgroup$ – zoidstar Oct 22 '19 at 11:00
  • $\begingroup$ In fact 'everything' could also be treated as a percentage. Rephrased this would be: '100% of the time I exaggerate 100% of what I say by 25%. By how much do I truly exaggerate?' $\endgroup$ – zoidstar Oct 22 '19 at 12:17
3
$\begingroup$

$20.7\%$ approximately.

If you exaggerate by $x\%$ then you are multiplying by $1 + \frac{x}{100}$.

We know that $x \times (1 + \frac{x}{100}) = 25$.

Solving for $x$ using the quadartic formula leads to the correct result.

Nice question. :)

$\endgroup$
1
$\begingroup$

Let $x$ be the fraction you exaggerate everything by.

Then $25\%$ is equal to $x$ exaggerated by $x$, so $x(1+x) = 25\%$.

Solving this quadratic equation yields $x = \frac{\pm\sqrt{2} - 1}{2}$.

So either you exaggerate everything by $20.71067811865\%$, or you exaggerate everything by $-120.71067811865\%$.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.