There are 3 solutions:
1. (3,3,3)
Since all of the variables can be equal and there are three fractions, then a, b, and c can all be equal to 3.
1/3+1/3+1/3=1
2. (2,4,4)
Since one fraction must exceed ⅓, the only other fraction that can be used is ½ because 1⁄1 will not give a solution under the initial conditions. Now you know you need two other fractions to solve the problem.
1/2+1/b+1/c=1
With hint one, we know that b and c can be equal.
1/4+1/4=1/2
Therefore, b and c are equal to 4.
3. (3,2,6)
Now, we can conclude that two fractions must exceed ¼. The only two variables that will satisfy this criteria are a = 2 and b = 3.
1/2+1/3+1/c=1
Therefore, 1/c=1/2-1/3=1/6
So c = 6.
1. (3,3,3)
Since all of the variables can be equal and there are three fractions, then a, b, and c can all be equal to 3.
1/3+1/3+1/3=1
2. (2,4,4)
Since one fraction must exceed ⅓, the only other fraction that can be used is ½ because 1⁄1 will not give a solution under the initial conditions. Now you know you need two other fractions to solve the problem.
1/2+1/b+1/c=1
With hint one, we know that b and c can be equal.
1/4+1/4=1/2
Therefore, b and c are equal to 4.
3. (3,2,6)
Now, we can conclude that two fractions must exceed ¼. The only two variables that will satisfy this criteria are a = 2 and b = 3.
1/2+1/3+1/c=1
Therefore, 1/c=1/2-1/3=1/6
So c = 6.