Analysis shows that nickel oxide has the formula $Ni_{0.98}O_{1.00}$. What fractions of nickel exist as $Ni^{2+} $and $Ni^{3+}$?

What i did:

Let the number of $Ni^{2+}$ and $Ni^{3+}$ atoms be $x$ and $y$ respectively

one atom/ion of $Ni^{2+}$ satisfies one $O^{2-}$ atom

$2 \over 3$ atom/ion of $Ni^{3+}$ one $O^{2-}$ atom

and then i wrote down the equations: $x + $$3 \over 2 $$y =1$ and $x+y=0.98$

Then i solved the equations to get the answers:

$x=0.94 $ $and$ $y=0.04$

Is what i did correct? If not then guide me how to solve the question

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    $\begingroup$ i am getting used to mathjax and markdown, so please if my question is tough to read someone edit it $\endgroup$ – Maxwell's Ghost Oct 17 '18 at 17:49
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    $\begingroup$ i don't know what is wrong with this question that nobody would answer it. I've given question and also said what my approach was. please someone answer $\endgroup$ – Maxwell's Ghost Oct 18 '18 at 3:17

What you have done seems to be correct. But you might want to convert those numbers to percentiles. I can tell you another method based on charge conservation.
Let us take 100 oxygen atoms and 98 Nickel atoms into our consideration.
Total negative charge$= 200$
Total positive charge$= 2x+3y$ where $x$ and $y$ are what you have assumed to be in the question . Now Net charge =0.Equate the positive and negative charges.
Also $x+y=98$. Solve them and you will get the same number. This of course has an high degree of
similarity to what you have done

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    $\begingroup$ yes, i agree with your last point. What i have done is also in a sense "charge conservation" $\endgroup$ – Maxwell's Ghost Oct 20 '18 at 18:19
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    $\begingroup$ yes , of course $\endgroup$ – optimus prime Oct 20 '18 at 18:20

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