<p><span style="color:#27ae60;"><span style="font-size:20px;">Solving the Problem</span></span></p>
<p>We know that the middle number in a list of 3 numbers will be the median, so our list would look something like this:</p>
<p>$x, 8, y$</p>
<ul>
<li>$x$ is the least number in the list</li>
<li>$y$ is the greatest number in the list</li>
</ul>
<p>We are told that the greatest number is 10 greater than the least number, so we can deduce that:</p>
<ul>
<li>$y = x + 10$</li>
<li>$x = y - 10$</li>
</ul>
<p>So, we can rewrite our list in terms of y:</p>
<p>$y-10, 8, y$</p>
<p>We also know the following about the relation between mean and sum:</p>
<p>$sum = mean * number of values$</p>
<p>Since we know the mean and the number of values, we can work out the sum:</p>
<p>$sum = 8 * 3$</p>
<p>$sum = 24$</p>
<p>We also know that 24 will be equal to the sum of every item in our list, so we can solve for y to find the greatest number in the list:</p>
<ul>
<li>$24 = (y-10) + 8 + y$</li>
<li>$24 = 2y - 10 + 8$</li>
<li>$24 = 2y - 2$</li>
<li>$26 = 2y$</li>
<li>$13 = y$</li>
</ul>
<p>So, the answer will be <span style="color:#27ae60;">13</span>.</p>