I have another problem

[Valentas]

There are two two-digit numbers. If bigger number we'd write in front of lesser and new 4-digit number divide from lesser two-digit number, than we get quotient 169 and residue of 12. If lesser two-digit number we'd write in front of bigger tow-diggit number and new 4-digit number divide from bigger two-digit number, than we'd get quotient 60 and residue 7. Find these two two-digit numbers.

My thoughts:

xy < qz

\(\displaystyle
\frac{qzxy}{xy}=169+12\) ARRAY ON BOTH. i DON'T KNWO HOW TO PUT IT ON LATEX.
\(\displaystyle \frac{xyqz}{qz}=60+7 \)

\(\displaystyle \frac{1000Q+100Z+10X+Y}{10X+Y} = 169+12\)
\(\displaystyle \frac{1000X+100Y+10Q+Z}{10Q+Z} =60+7 \)

any help ? I hope I'm not too pesky.

 

[tkhunny]

\(\displaystyle \frac{1000Q+100Z+10X+Y}{10X+Y} = 169+\frac{12}{10X+Y}\)

\(\displaystyle \frac{1000X+100Y+10Q+Z}{10Q+Z} =60+\frac{7}{10Q+Z} \)

\(\displaystyle X, Y, Z, Q \in \{0,1,2,3,4,5,6,7,8,9\}\)

What's your plan? Seems like there's quite a bit of information.

 

[Valentas]

\(\displaystyle \frac{1000Q+100Z+10X+Y}{10X+Y} = 169+\frac{12}{10X+Y}\)

\(\displaystyle \frac{1000X+100Y+10Q+Z}{10Q+Z} =60+\frac{7}{10Q+Z} \)

\(\displaystyle X, Y, Z, Q \in \{0,1,2,3,4,5,6,7,8,9\}\)

What's your plan? Seems like there's quite a bit of information.

I did that but I don't know yet how to move forward. Tried to multiply both sides from denominator but I got only more x,y,q,z