3/5 of the people at a funfair were children. 3/4 of the remaining people were men. There were 140 more children than women. How many people went to the funfair?

If there were x people in all, then

men = (3/4)(2/5)x = 3/10 x
3/5 x = 140 + (1 - 3/5 - 3/10)x = 140+x/10
6x = 140+x
5x = 1400
x = 280

check:
3/5 of 280 = 168
3/4 of 280-168 = 84
women = 168-140 = 28

168+84+28 = 280

I got 280 as well

Let's break down the problem step-by-step:

Step 1: Let's assume the total number of people who went to the funfair is "x".
Number of children = (3/5) * x
Number of adults = x - (3/5) * x = (2/5) * x

Step 2: From the remaining people, 3/4 were men.
Number of men = (3/4) * ((2/5) * x) = (6/20) * x = (3/10) * x

Step 3: The number of women is 140 less than the number of children.
Number of women = Number of children - 140
Number of women = (3/5) * x - 140

Step 4: Given that the number of children is 140 more than the number of women:
Number of children = Number of women + 140
(3/5) * x = (3/5) * x - 140 + 140
(3/5) * x = (3/5) * x

Step 5: Since the number of children and the number of women are equal, we can equate the expressions and solve for x.
(3/5) * x = (3/5) * x
This equation is satisfied for any value of x.

Step 6: Given that x represents the total number of people who went to the funfair, the value of x can be any positive number.

Therefore, there is not enough information given in the problem to determine the exact number of people who went to the funfair.

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

Let's assume the total number of people who went to the funfair is "x".

From the information given, we know that 3/5 of the people were children. So, the number of children at the funfair can be calculated as (3/5)x.

The remaining people would be (2/5)x, which includes both men and women.

Now, we are told that 3/4 of the remaining people were men. So, we can calculate the number of men as (3/4) * (2/5)x.

The number of women would be the remaining people after subtracting the number of men, which is (2/5)x - (3/4) * (2/5)x.

According to the problem, there were 140 more children than women. This can be written as (3/5)x = (2/5)x - (3/4) * (2/5)x + 140.

To solve this equation, we can simplify it as follows:

(3/5)x = (2/5)x - (3/4) * (2/5)x + 140

Multiplying through by 5 to clear the denominators gives:

3x = 2x - (3/4)*2x + 700

Simplifying further:

3x = 2x - (6/4)x + 700
3x = 2x - (3/2)x + 700
3x = (4/2)x - (3/2)x + 700
3x = (1/2)x + 700

Subtracting (1/2)x from both sides gives:

(3/2)x = 700

Finally, multiplying through by 2/3 gives:

x = 700 * (2/3)

Evaluating the right side gives:

x = 466.67

Since we cannot have a fraction of a person, we can round the answer to the nearest whole number. Therefore, approximately 467 people went to the funfair.