<p>Picking numbers in percent problems: If the word “percent” appears in a problem it’s usually a great idea to choose the number 100. This often works even when there is no variable in the problem.</p>
<p>Here is a Level 5 example:</p>
<p>If Matt’s weight increased by 30 percent and Lisa’s weight decreased by 20 percent during a certain year, the ratio of Matt’s weight to Lisa’s weight at the end of the year was how many times the ratio at the beginning of the year?</p>
<p>Try to solve this problem by choosing both Matt’s weight and Lisa’s weight to each be 100 at the beginning of the year.</p>
<p>What happens if you pick numbers other than 100 here?</p>
<p>Also try to solve this algebraically without picking numbers.</p>
<p>Which method do you prefer?</p>