Largest value of (x+y)

[Zzzz]

$x,y \in \mathbb N$. Find the largest value of $(x+y)$ such that \[20x+11y=2011\]

made by Sakal Roy- Khulna Math Club

[Sudip Deb new]

The answar is 182.818181... . When the y is 182.81818... and the x is o . We divide by the smaller number which is 11 . If we divide by the 20 or both the answar will be smaller then 182.818181... . So thats the answar .

[Zzzz]

$x,y \in \mathbb N$

[Avik Roy]

$182$ is the correct answer.
if $(100,1)$ is the initial solution then
$x_n = 100 - 11n$
and $y_n = 1 +20n$
Then $x_n + y_n = 101 + 9n$
The largest $n$ that keeps $x$ in $\mathbb N$ is $9$. So the largest value of $x+y$ is $182$

[faisalnir]

$$20x+11y=2011$$
then $$11(x+y)=2011-9x$$
when $$x=1$$ then $$11(x+y)=2002$$ which is largest...
so ans:$$182$$