Answer :
[tex]\dfrac{k}{27}>\dfrac{2}{3} \wedge \dfrac{k}{27}<\dfrac{8}{9}\\
k>18 \wedge k<24\\
k\in(18,24)\\\\
k\in(18,24) \wedge k\in \mathbb{Z}\\
k\in\{19,20,21,22,23\}\\\\
19+20+21+22+23=\boxed{105}
[/tex]
so we want to make them have the same denomenator so
k/27
2/3 times 9/9=18/27
8/9 times 3/3=24/27
so k/27>18/27 and k/27<24/27 or
18/27<k/27<24/27
the possible numbers for k are 19,20,21,22,23
so the sum of the positive integers could be any positive whole numbers (1,2,3,4, etc) that add up to 19,20,21,22,23 exg 10,9 10,10 10,11 20,2 21,2 etc
k/27
2/3 times 9/9=18/27
8/9 times 3/3=24/27
so k/27>18/27 and k/27<24/27 or
18/27<k/27<24/27
the possible numbers for k are 19,20,21,22,23
so the sum of the positive integers could be any positive whole numbers (1,2,3,4, etc) that add up to 19,20,21,22,23 exg 10,9 10,10 10,11 20,2 21,2 etc
