two whole numbers whose sum is 72 cannot be in the ratio

Question

two whole numbers whose sum is 72 cannot be in the ratio

 

 

answer 3:2

Answer 1

There are many answers to this question.

 

How would we split 72 into the ratio a:b where a,b are integers and relatively prime (ie do not have a common factor)

 

The split would be 72*a/(a+b) and 72*b/(a+b).  Since a and b are relatively prime, (a+b) must divide 72 for these numbers to be integers.

 

One answer is 3:2 as you have noted since 3,2 are relatively prime and 3+2=5 does not divide 72.