Answer:
Zog:75
Zoz: 100
Zob :150
Zop:175
Zod :250
Step-by-step explanation:
Smallest island:
not Zoz
not Zop (100 people more than smallest island)
not Zob (1.5 times larger than one of the other islands)
not Zod (the largest island)
Zog is the smallest island (process of elimination)
use clue #1 Pzog=0.1Ptotal
Pzog=0.1*750
Pzog=75
Zog has 75 Zoxians living on it
now lets use clue #5
Pzop=Pzog+100
Pzop=75+100
Pzop=175
Zop has 175 Zoxians living on it
Lets use clue #3
lets find the fraction of the population living on Zog 75/750=1/10
lets find the fraction of the population living on Zop 175/750=7/30
there is an island 2 times larger (2/10)than zog (1/5)
there is an island with a population of 2 times larger 75*2=150
there is an island with 1/3 of total Zox population
this island has 250 people on it
now the last island has 750-75-175-150-250= 100 people living on it
now, lets use clue #4 to find which island is Zob:
Zog:75
Unknown 3: 100
Unknown 1:150
Zop:175
Unknown 2:250
Unknown island 1 is 1.5 times larger than Unknown 3,
thus Unknown 1 is Zob
Zog:75
Unknown 3: 100
Zob 1:150
Zop:175
Unknown 2:250
Zod is largest, so unknown 2 is Zod
Zog:75
Unknown 3: 100
Zob 1:150
Zop:175
Zod :250
by process of elimination, unknown 3 is Zoz
Zog:75
Zoz: 100
Zob 1:150
Zop:175
Zod :250
