Where k is some solvable constant:
H e n s ∗ D a y s = k ∗ E g g s {\displaystyle Hens*Days=k*Eggs}
1 1 2 ∗ 1 1 2 = k ∗ 1 1 2 {\displaystyle 1{\frac {1}{2}}*1{\frac {1}{2}}=k*1{\frac {1}{2}}}
k = 1 1 2 {\displaystyle k=1{\frac {1}{2}}}
1 ∗ 1 = 1 1 2 E g g s {\displaystyle 1*1=1{\frac {1}{2}}Eggs}
E g g s = 1 1 1 2 = 1 3 2 = 2 3 {\displaystyle Eggs={1 \over {1{\frac {1}{2}}}}={1 \over {3 \over 2}}={2 \over 3}}