If she is setting up a proportion to find the percent, the value of m would be any variable and the value of n would be 100. When she solves the problem, m=65%.
13/20 is part out of whole. The rest of the proportion will be "percent out of 100"; since we don't initially know the percent, we use a variable. Thus we have
13/20 = m/100
Cross multiply:
20*x = 13*100
20x = 1300
Divide both sides by 20:
20x/20 = 1300/20
x = 65
