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If I have $22x = 23y = 24z$ and $x+y+z = 3865$ how to obtain the values of $x$,$y$ and $z$ ?

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How about substitution? – Andy Jan 2 '11 at 11:25
Indeed substitution works like a charm :) – Quixotic Jan 2 '11 at 11:57
up vote 3 down vote accepted

use $ y = \frac{22}{23}x$ and $z = \frac{22}{24}x$ in last equation.

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You can use $\TeX$ markup to beautify your equations by putting $-marks around them. – FUZxxl Jan 2 '11 at 11:29
got it, thanks. – 911 Jan 2 '11 at 11:44
also you can right-click on any $\TeX$, select Show Source, and see how it was done. FUZxxl got his fractions using the \frac command. For this answer, they are clear enough, but it is a good way to learn. – Ross Millikan Jan 2 '11 at 11:59
cool...................... – 911 Jan 2 '11 at 12:28

First, try to express $y$ and $z$ by $x:$

$$22x = 23y\Leftrightarrow y = \frac{22}{23}x$$

$$22x = 24z\Leftrightarrow z = \frac{11}{12}x$$

Then put this into your term to archieve a value for $x:$

$$x+y+z=3865\Leftrightarrow x+\frac{22}{23}x+\frac{11}{12}x=3865$$

Now you have the value of $x.$ To figure out $y$ and $z$ is left as an exercise to you.

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