<p>1) 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>2) How many positive integers less than 1,000 are multiples of 5 and are equal to 3 times an even integer?</p>
<p><em>These are grid in questions</em> Can you explain how to approach these questions please?</p>
<p>So, a/b=.625 which is 5/8. Then just find unsimplified fractions that are equal to 5/8. Add a and b to see if they’re under 1000. If you multiply 5/8 by 76/76 you get 380/608. 380+608<1000. The max value of b is 608.</p>
<p>I’m not sure on the second one, but the set of numbers that are multiples of 5 and 3 times an even integer is {30,60,90,120,150…990} Each 10 has 3 integers that work. So you have 10s, 100s, 200s 300s, 400s, 500s 600s, 700s, 800s, and 900s with 3 integers that work. 10x3=30. </p>
<p>I’m not sure if this one is right, just best guess.</p>
<p>for the second one the answer is suppose to be 33 "/, and yea thanks for explaining the first one, I get it now!</p>
<p>1) Solve a/b=.625 for a. So, a=.625b. Substitute this value for a in the inequality.
.625b+b less than 1000
1.625b less than 1000
b less than 615.3846…
b, since it is an integer, is 615</p>
<p>2) As bakere19 has stated, you need to find the multiples of 30 that are less than 1000. The largest multiple of 30 less than 1000 is 990. 990 divided by 30 is 33. So, the answer is 33.</p>