[KungKemi]

Similar to a previous post, I also came across the following stoichiometry question in an RSC journal:

"A mixture contains KClO, MnCl₂ and KMnO₄. What must the percentage of potassium be to have the chlorine percentage equal to the percentage of oxygen?"

I have been working this question through for quite a while now and have come up with the following 5 systems:

39.10a + 39.10c = x
54.94b + 54.94c = y
35.45a + 70.9b = z
16.00a + 64.00c = z
x + y + 2z = 100

As can be seen, I have a total of 6 unknowns: a = mol KClO, b = mol MnCl₂, c = mol KMnO₄, x = mass of K,
y = mass of Mn, and z = mass of O or mass of Cl.

Nonetheless, since I only have 5 unique expressions; the following question is unsolvable with the method which I am currently using.

I was just wondering if I was missing something or if the following question is indeed unsolvable?

n.b. I mainly want to know if the following question is solvable. I do not want to have any hints.

Thank you,
KungKemi

[Borek]

Solution exists, but it is not what you think it is.

You definitely started right by writing system of equations, but you are expecting wrong kind of a solution.

No need to use colors in posts, they are perfectly readable in black.

[KungKemi]

Solution exists, but it is not what you think it is.

You definitely started right by writing system of equations, but you are expecting wrong kind of a solution.

No need to use colors in posts, they are perfectly readable in black.

Okay, thank you Borek. Also, I was wondering if you would be able to share the answer which you arrive at (just so I can compare my answer in future if I arrive at one), as the source where I found this question does not list solutions.

[AWK]

If you look at KClO, it contains lower mass of oxygen then mass of chlorine. KMnO₄ contains only oxygen without chlorine. It means you can prepare mixture of both salts that fulfill requirement that mass of O equals to mass of Cl (equivalent to %O=%Cl). After addition of  MnCl₂ you should increase oxygen by adding more KMnO₄.
Hence this is multisolution problem.
Check my reasoning starting from 1 mole of KClO and calculate how many moles of KMnO₄ (without addition of any MnCl₂) fulfills condition: %O=%Cl.