Thread: can we solve for Z if we know X? [admin note:not solved]

Hi there,

Please help I haven't done maths since school and I wasn't that good back then but if any of you could help me with this basic equation that would be awesome as I need to use it in some work I'm doing. Thanks alot.


If 6Y-Z=X and Y/Z is a whole number can we solve for Z if we know X?

Ie. 6(34)-17=187 (you can see 34 or 'Y' divided by 17 or 'Z' is 2 - a whole number)

Originally Posted by Not2l8

Hi there,

Please help I haven't done maths since school and I wasn't that good back then but if any of you could help me with this basic equation that would be awesome as I need to use it in some work I'm doing. Thanks alot.


If 6Y-Z=X and Y/Z is a whole number can we solve for Z if we know X?

Ie. 6(34)-17=187 (you can see 34 or 'Y' divided by 17 or 'Z' is 2 - a whole number)

Hi Not2l8,

Welcome to MHF!

This problem is a little more tricky than it seems. I don't have a full solution for you, but a partial one if we make certain assumptions.

Let's rearrange the initial equation: . I just divided through by "z". So if we are assuming that "y/z" is a whole number, this implies that "x/z" is as well. Why? Well look at the left hand side of the new equation I wrote: . Since y/z is whole, 6 times this whole number is still a whole number, and subtracting 1 from that still is a whole number. Thus x/z is a whole number.

Grr, sorry I have to run now but maybe this is somewhat helpful. When I get back in a few hours I'll see if you've gotten help and if not I'll try to finish the problem.

Thanks Jameson, I don't want to confuse you guys even more but if I know X and I'm trying to find Z in the following equation as described above

'6Y+/-Z=X'

Does it help if we know

A) Y is a multiple of Z unless Y=0
B) Z is a multiple of 6 +/-5.
C) Z is an odd whole number

Example. If X is 187

Then 6(34)-17=187

You can see
A) 34 or 'Y' is a multiple of 17 or 'Z'
B) 17 or 'Z' is equal to 2x6+5
C) 17 or 'Z' is odd.

Another example. X is 175

Then 6(30)-5 = 175

A) 30 or 'Y' is a multiple of 5 or 'Z'
B) 5 or 'Z' is equal to 0x6+5
C) 5 or 'Z' is odd

Any help with this would be great.
If it can be solved, ie. If a real answer for 'Z' can be found if I know 'X' it will have a pretty awesome application which I will explain afterwards.

Even if you can't solve it would you let me know if you think it can be solved and maybe another forum I could post it on. Thanks again for your help guys.

Hey again. I've moved this post to Number Theory because it is more complicated than basic algebra. The topic of finding solutions dealing with only whole numbers can be very complicated. I can't think of a way to solve this right now but I promise you this forum has many people who can. Just be a little patient and someone will make this look easy