When dealing with weighted averages, how do you solve for X?

$$ \frac{( 84X) + (40*16)}{100} = 10.5 . $$

  • 2
    $\begingroup$ This is just a linear equation in $X$. You remember your algebra and perform the same operations on each side of the equation toward the goal of isolating $X = ...$. I edited your question to format the mathematics - that might help you. If you're really stuck and need to do this just once, try guess-and-check. When you're done, answer your own question (that's allowed on this site). $\endgroup$ – Ethan Bolker Dec 26 '16 at 19:34
  • $\begingroup$ @EthanBolker Sadly I've forgotten far too much of my algebra to figure it out that way, and Google hasn't been much help in that regard ;-) $\endgroup$ – Chaya Cooper Dec 26 '16 at 20:10

Here are the steps:

  1. Remove the fraction by multiplying both sides by $100$.

  2. Isolate the $X$ term by subtracting the $(40*16)$ from both sides.

  3. Remove the coefficient of $X$ by dividing both sides by $84$.

  • $\begingroup$ Thank you for jogging my long-dormant High School math memory with step 3 :) $\endgroup$ – Chaya Cooper Dec 26 '16 at 20:50
  • $\begingroup$ @ChayaCooper Lol, no problem mate ;) $\endgroup$ – Simply Beautiful Art Dec 26 '16 at 20:51
  • $\begingroup$ I'm curious what I'm doing wrong that I'm ending up with 4.88 instead of 5? $\endgroup$ – Chaya Cooper Jan 2 '17 at 19:25
  • $\begingroup$ @ChayaCooper And as written, that should be the correct answer. I'm not sure how one would be getting $5$ as an answer. $\endgroup$ – Simply Beautiful Art Jan 2 '17 at 19:26

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