The number of people living in a town is found to be perfect cube. We know that the numbers of men in the town are15653, and the numbers of women in the town are25739. By an odd coincidence, we count and find that the number of children in the town is also a perfect cube. If we give you a hint that this number is cube of 21, then find the number of people living in the town?Also find the cube root of number of people.
Answers
Answer:
The smallest possible number of children in the town is 9261.
Step-by-step explanation:
Step 1
Total population of the town is a perfect cube.
Number of men in the town = 15653
Number of women in the town = 25739
Step 2
It is given that the number of children in the village is also the perfect cube, and is more than 9260.
Let us first find the values of perfect cubes more than 9260.
Step 3
Cube root of 9260 = 20.999244114894 and the perfect cubes more than 9260 will be the cubes of
all integers more than 20.999244114894, i.e. 21
3
, 22
3
, 23
3
, etc.
Step 4
The population of children will be the smallest value out of 21
3
, 22
3
, 23
3
, etc, for which the total
population of the village is a perfect cube.
Step 5
Let us see if the population of the children can be 21
3
(= 9261). In this case, the total population of
the village will be = 15653 + 25739 + 21
3
= 15653 + 25739 + 9261
= 50653
Since the cube root of 50653 is 37, which is an integer, the total population of the village in this
case is indeed a perfect cube.
Step 6
Therefore, the smallest possible number of children in the village is 21
3 = 9261.