I am trying to solve this problem
W is a positive integer when divided by 5 gives remainder 1 and when divided by 7 gives remainder 5. Find W.
I am referring back to an earlier post I made. Now I am attempting to solve it that way.
We know that $w\equiv1(mod~5)$ $w\equiv5(mod~7)$
$w=7r+5$
$w=5r+5+2r$
Since $5r+5$ is divisible by 5
$w=5(r+1)+2r$ this shows the remainder is $2r$
Now $2r$ divided by 5 gives a remainder 1 , thus giving the equation
$2r = 5k + 1$ or $r=\frac{5k+1}{2}$
Putting r back in $w=7r+5$ we get
$2w = 35k + 12$
So I guess $w= \frac{35+12}{2} = 23.5$
This is wrong and the answer is suppose to be 26. Any suggestions what I might be doing wrong ? or anything that I might be missing ?
Edit: The problem was in calculation
$w= \frac{35+17}{2} = 26$