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I haven't done Math in a very long time, or at least something beyond 5th grade stuff, so I'm perplexed by this question.

Given the following formula, solve for X:

Y = X + (X * .0635) where Y = 19892

At first I tried dividing both sides by .0635, but that made Y unreasonably high. Next, I found an online calculator that gave me the answer, but it didn't show the steps. I need to be able to see the steps so I understand how the answer was achieved.

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  • $\begingroup$ This is a quadratic equation. You'll need the quadratic formula. $\endgroup$
    – Sean Roberson
    May 2, 2022 at 12:35
  • $\begingroup$ @SeanRoberson I see no exponents in the above. This is linear. $\endgroup$
    – JMoravitz
    May 2, 2022 at 12:38
  • $\begingroup$ It's a first-order equation actually. $X+0.635X=1X+0.635X=1.635X=Y$. Now you can divide both sides of the equation. $\endgroup$
    – drC1Ron
    May 2, 2022 at 12:38
  • $\begingroup$ Recognize that $X+(X\cdot .0635) = (X\cdot 1) + (X\cdot .0635)$ which you can factor out a common $X$ (essentially the reverse of the distributive property: $(a+b)c = ac+bc$). Here we have $X+(X\cdot .0635) = X(1+.0635)$ $\endgroup$
    – JMoravitz
    May 2, 2022 at 12:40
  • $\begingroup$ ... whoops, there is a 0.0635 rather than 0.635 coefficient $\endgroup$
    – drC1Ron
    May 2, 2022 at 12:41

1 Answer 1

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You need to be careful that you have divided $\textit{everything}.$

When dividing you should reach this.

$$y = x + 0.0635x \\ \implies \frac{y}{0.0635} = \frac{x}{0.0635}+x $$

However, the more useful approach in general is to factorise. In particular, here we have that $x$ is a common factor and so $x+0.635x= (1+0.0635)x=1.0635x $

So, $$19892=y=1.0635x \\ \implies x=\frac{19892}{1.0635}=18704.3... $$

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    $\begingroup$ My number was actually .0635, but once I made that adjustment this worked perfectly. I appreciate the explanation, it helped a lot! $\endgroup$
    – Johnny Bones
    May 2, 2022 at 12:47

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