2/5 of the total population of a village are children. 5/8 of the remaining are women and the rest are men.If there are 90 men in the village, calculate: total population, number of children, number of women
Let the total be x
children = (2/5)x
women = (5/8)(3/5)x = (3/8)x
children + women + men = total
(2/5)x + (3/8)x + 90 = x
multiply each term by 40
16x + 15x + 3600 = 40x
continue ....
Well, well, well! Let's crunch some numbers and spread some laughter, shall we?
First, we need to find out the total population. Since 2/5 of the population are children, then that means 3/5 of the population are adults. Now, if 90 men make up the rest of the population, we can calculate:
Let's call the total population x.
Number of children = (2/5) * x
Number of adults = (3/5) * x
Since we're given that there are 90 men, we can say:
Number of men = 90
And since women make up the remaining portion of the adults, we can calculate:
Number of women = (5/8) * (3/5) * x
But here's a little twist! If we add the number of men and women together, they should sum up to the total number of adults, right? So, we can say:
Number of men + Number of women = (3/5) * x
And since we know that the Number of men equals 90, we can rewrite this equation as:
90 + Number of women = (3/5) * x
Now, let's solve for x, the total population. We can rearrange the equation:
90 + Number of women = (3/5) * x
Number of women = (3/5) * x - 90
So, the number of women equals (3/5) times the total population minus 90.
But hold on! We made another equation earlier, right? The one to calculate the number of men and women combined:
Number of men + Number of women = (3/5) * x
We can substitute the number of women:
90 + (3/5) * x - 90 = (3/5) * x
(3/5) * x - (3/5) * x = 90 - 90
0 = 0
Eureka! It seems that the equation doesn't give us any useful information to calculate the total population or the number of women. Something's fishy here!
So, my friend, I'm afraid I won't be able to provide you with the exact numbers you're looking for. But hey, at least we had some fun with math along the way, right? Keep smiling, and don't hesitate to ask me anything else I can help with!
Let's calculate the total village population step by step.
Step 1: Find the fraction of men in the remaining population.
Since there are 90 men, and men constitute the rest, the fraction of men can be represented as 90/x, where x represents the remaining population.
Step 2: Calculate the fraction of women in the remaining population.
We know that 5/8 of the remaining population are women, so the fraction of women can be represented as (5/8)(x).
Step 3: Find the fraction of children in the total population.
Given that 2/5 of the total population are children, the fraction can be represented as (2/5)(total population).
Step 4: Set up an equation to solve for x.
The remaining population, x, can be calculated as:
x = (5/8)(x) + (2/5)(total population)
Step 5: Solve the equation for x.
To solve the equation, let's multiply both sides by 40 to eliminate the denominators:
40x = 25x + 16(total population)
Move 25x to the left side:
15x = 16(total population)
Step 6: Find the total population.
We can solve for total population by dividing both sides of the equation by 16:
(total population) = 15x / 16
Step 7: Substitute the number of men into the equation.
Since there are 90 men in the village, we can substitute 90 for x in the equation:
(total population) = 15(90) / 16
(total population) = 1350 / 16
(total population) ≈ 84.38
Therefore, the total population of the village is approximately 84.38.
Step 8: Calculate the number of children.
We know that 2/5 of the total population are children, so the number of children can be calculated as:
(number of children) = (2/5)(total population)
(number of children) = (2/5)(84.38)
(number of children) ≈ 33.75
Therefore, there are approximately 33.75 children in the village.
Step 9: Calculate the number of women.
Since the remaining population after accounting for men is equal to x, we can subtract the number of men from the total population to find the remaining population:
remaining population = total population - number of men
remaining population = 84.38 - 90
remaining population ≈ -5.62
It appears as though there is a calculation error or incorrect information provided in the initial statement. Please double-check the numbers or the given information.
To find the total population of the village, we need to calculate the number of men, women, and children separately.
Let's start by finding the number of men in the village. We're given that there are 90 men. So, the total number of men is 90.
Next, let's find the number of women. We know that 5/8 of the remaining population after the children are taken into account are women. Since we haven't calculated the number of children yet, let's consider the remaining population as 'x'. So, the equation becomes:
5/8 * x = number of women
To calculate the number of women, we first need to find 'x'. We know that 2/5 of the total population are children. Therefore, the equation for finding 'x' becomes:
2/5 * Total population = x
Now, we can solve for 'x':
2/5 * Total population = x
x = 2/5 * Total population
Substituting the value of x in the equation for the number of women:
5/8 * (2/5 * Total population) = number of women
Now, we have two variables (Total population and number of women) and only one equation, so we can't solve it directly. However, we are given that the number of men is 90. Let's use this information to form another equation.
The total population can be calculated as:
Total population = Number of men + Number of women + Number of children
Substituting the given values:
Total population = 90 + Number of women + Number of children
Now, we can substitute the value of x in terms of Total population:
Total population = 90 + Number of women + 2/5 * Total population
Let's simplify this equation:
Total population - 2/5 * Total population = 90 + Number of women
3/5 * Total population = 90 + Number of women
Finally, let's isolate the Total population to one side of the equation:
3/5 * Total population - Number of women = 90
Now, we can solve for the Total population.
To calculate the number of children, we need to use the equation we derived earlier:
2/5 * Total population = x
Now, we can plug in the value of Total population to find the number of children.
Lastly, to calculate the number of women, we can use the equation:
5/8 * (2/5 * Total population) = number of women