There were a some men, women , children in a hall.there 1 1/4 times as many men as women,and the ratio of number of women to the number of children is 8:5.when 105 more children entered the hall, the ratio of men to the children changes to 3:2. find the ratio of men to children at first?how many men and women were there in the hall. It gives negative result. Hope may be some mistakes in numbers. Pls guide me

Question

There were a some men, women , children in a hall.there 1 1/4 times as many men as women,and the ratio of number of women to the number of children is 8:5.when 105 more children entered the hall, the ratio of men to the children changes to 3:2. find the ratio of men to children at first?how many men and women were there in the hall. It gives negative result. Hope may be some mistakes in numbers. Pls guide me

Answer 1

let the number of women be x

then the number of men = 1.25x

women to children = 8:5
= x : 5x/8

after 105 children come
number of children = 5x/8+108

now :
1.25x : (5x/8+105) = 3 : 2
1.25x/(5x/8+105) = 3/2
15x/8 + 315 = 2.5x
1.875x + 315 = 2.5x
x = 504

So we had 504 women, 630 men and 315 children
original ratio of men : children = 630:315 = 2 : 1

check:
after new kids came, children is 420

ratio of men : children = 630 : 420 = 3 : 2

My answers are correct

Answer 2

To solve this problem, let's break it down step by step.

1. Let's start by assigning variables to the unknown quantities. Let's call the number of men M, the number of women W, and the number of children C.

2. We are given that there are 1 1/4 times as many men as women. This can be represented as:M = (1 1/4)W.

To simplify this, let's convert the mixed fraction 1 1/4 to an improper fraction. 1 1/4 = 5/4.

Therefore, M = (5/4)W.

3. We are also given that the ratio of women to children is 8:5. This can be represented as: W:C = 8:5.

We can rewrite this ratio as W = (8/5)C.

4. Next, we are told that when 105 more children entered the hall, the new ratio of men to children is 3:2.

Since the total number of children changed, let's represent the new number of children as (C + 105).

Now we have M:(C + 105) = 3:2.

5. Let's substitute the expressions for M and W from step 2 and step 3 into the equation from step 4.

We have (5/4)W: (C + 105) = 3:2.

Substituting (8/5)C for W, we get (5/4)(8/5)C: (C + 105) = 3:2.

Simplifying, we have (4/1)C: (C + 105) = 3:2.

Cross-multiplying, we get 8C + 840 = 6C + 315.

6. Solving for C, we can subtract 6C from both sides and subtract 840 from both sides:

8C - 6C = 315 - 840.

7. Simplifying further, we get 2C = -525.

This leads to a negative result, which suggests that there may be an error in the given information or the calculations made so far.

Please double-check the information provided or the steps followed to ensure accuracy.

If you have any further questions or need clarification, please let me know.