<p>If a and b are integers such that a + b < 1000 and a/b = 0.625, what is the greatest possible value of b?</p>
<p>How do I approach this problem?</p>
<p>I got 608. This is how I did it
Solve for a in the second equation
You get a = .625b
plug it into the first equation
1.625B < 1000 is what you get
now you B < like... 615.38 blah blah.
Now you would think the answer is 615 because its the closeset integer. But try plugging B = 615 in the second equation. A becomes a non-integer. Keep plugging while going down and you get 608.. i hope thats the answer.</p>
<p>We know a/b = 5/8. Since a and b are integers, a+b is multiple of 13.
We want to chose a+b to be as large as possible, but less than 1000.</p>
<p>So we chose a+b to be 988, the largest multiple of 13 less than 1000, which forces b to be 608.</p>