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
To solve this problem, we can use a step-by-step approach.
Step 1: Let's assume the total number of people at the funfair is 'x'.
Step 2: We know that 3/5 of the people were children. So, the number of children at the funfair would be (3/5)x.
Step 3: The remaining people (2/5x) would be adults.
Step 4: According to the problem, 3/4 of the remaining people were men. So, the number of men would be (3/4)(2/5x) = (3/10)x.
Step 5: It is given that there were 140 more children than women, which means the number of children minus the number of women is 140. We can write this as (3/5)x - (x - (3/10)x) = 140.
Step 6: Simplifying the equation, we get (3/5)x - (7/10)x = 140.
Step 7: Combining like terms, we have (1/10)x = 140.
Step 8: Multiplying both sides by 10, we find x = 1400.
Therefore, the total number of people who went to the funfair is 1400.