The sum of three mixed numbers is 22 1/20. two of the numbers are 8 1/2 and 5 1/4. what is the third number?

Make all mixed number improper fractions first...

rule:  a b/c=(ac+b)/c

22 1/20=8 1/2+5 1/4+n

441/20=17/2+21/4+n  make all have a common denominator of 20

441/20=170/20+105/20+20n/20 multiply both sides by 20

441=170+105+20n  combine like terms

441=275+20n subtract 275 from both sides

166=20n  divide both sides by 20

n=166/20  and we can convert this back to a mixed number...

n=(160+6)/20

n=8+6/20

n=8 3/10