$X$ and $Y$ are two-digit numbers. If $Y=2X+2$ and $Y=2X$ in decimal and octal system respectively, and unit digits of $X$ and $Y$ are $5$ and $2$ respectively, then how to find $X+Y$ in decimal number system?
My attempt:
I tried representing the two numbers in decimal as $(10a+5,10b+2)$ and in octal as $(8a+5,8b+2)$ and then tried to manipulate with according to the conditions $Y=2X+2$ and $Y=2X$, but they only give me one equation $b-2a=1$, how to get $10a+10b+7$(the sum of $X+Y$ in decimals) from these?