<p>The following two problems are grid-in questions at the end of a section.
Any help? I can do them, but a long, painful way.... :</p>
<p>If a and b are integers such that a + b < 1000 and (a/b) = .625, what is the greatest possible value of b?</p>
<p>How many positive integers less than 1,000 are multiples of 5 and are equal to 3 times an even integer?</p>
<p>Thanks in advance!</p>
<p>a / b = 5 / 8
a = 5b / 8
13b / 8 < 1000
b <= 615</p>
<p>The smallest number smaller than 615 that is divisible by 8 is 608.</p>
<p>The number has to be a multiple of both 5 and 6. This includes all the multiples of 30 from 30 to 990. There are [1000/30], or 33, of these.</p>
<p>1) Answer: 608.</p>
<p>Explanation: since a/b = 5/8 then a + b must be a multiple of 5/8. basically just plug in numbers.</p>
<p>5/8 x 76/76 = 380/608 and since a + b <1000 then 380+608=988 which is less than 1000. Note: if you tried 5/8 x 77/77 since you would get 385/616 which would add up to 1001 which is over.</p>
<p>Since your trying to find the "great possible value of b" then b = 608.</p>
<p>2) Answer: 33</p>
<p>Explanation: Since it has to be a multiple of 5 and 3 times an even integer then find all the numbers less than 100 that are a multiple of 15 and an even integer.</p>
<p>First, divide 1000/15 which is 66.66667. So we know that 15 x 66 is the biggest even integer. The smallest is 15 x 2. So the even integers from 2 to 66 inclusive are the answers to the quesiton. To find the number of integers from 2 to 66 that are even divide 66/2 which is 33. So 33 integers satisfy the question.</p>
<p>Lol, you gave a much more concise and lucid explanation than I did. Good Job Begoner.</p>
<p>wow, i'd have trouble on this actually.
thanks guys =p</p>