Five-eights of the population of a village are men, one-sixth are children and the rest, 500 in number are women. How many children are there?
i dont understand
(5/8)x + (1/6)x + 500 = x
(15/24)x + (4/24)x + 500 = x
(19/24)x + 500 = x
500 = (5/24)x
500 / (5/24) = x
500 * (24/5) = x
2,400 = x
~~~~~~~~~~~~~~~~~~~~~~~~~
(1/6) * 2,400 = __________ children
To find the number of children in the village, we need to determine what fraction of the population is represented by the given information.
According to the problem, five-eighths of the population are men, one-sixth are children, and the remaining number (500) are women.
Let's denote the total population of the village as x.
Fraction of men = 5/8
So, number of men = (5/8) * x
Fraction of children = 1/6
So, number of children = (1/6) * x
We also know that the number of women is 500.
Therefore, we can write the equation:
(5/8) * x + (1/6) * x + 500 = x
To simplify this equation, we can multiply through by 24 to eliminate the fractions:
5 * 3x + x + 12000 = 24x
15x + x + 12000 = 24x
16x + 12000 = 24x
12000 = 8x
Dividing both sides by 8:
1500 = x
So, the total population of the village is 1500.
Now, we can substitute this value back into the equation to find the number of children:
Number of children = (1/6) * 1500
Number of children = 250
Therefore, there are 250 children in the village.