Final answer:
The total number of people at the football match can be calculated using algebra by setting up equations based on the given relationships between the numbers of men, women, and children. Solving these equations reveals there were 450 people at the match.
Step-by-step explanation:
The problem is a classic algebra word problem where we are given specific information about the relationship between the number of men, women, and children at a football match and asked to determine the total number of people present. Let's represent the number of women with the variable 'W'. According to the problem, there are 250 more men than women, which can be represented as 'M = W + 250'. The number of children is twice the number of women, which is 'C = 2W'. The problem also states that the number of men is twice the number of women and children combined, leading to 'M = 2(W + C)'.
By substituting the values of 'M' and 'C' into 'M = 2(W + C)', we can solve for 'W', and consequently, determine the values of 'M' and 'C'. After finding these values, we can calculate the total number of people at the match by adding the number of men, women, and children.
Step by step, the solution is as follows:
- M = W + 250 (1)
- C = 2W (2)
- M = 2(W + C) (3)
Substituting (1) and (2) into (3) gives:
M = 2(W + 2W) = 2(3W) = 6W
Comparing it with equation (1) we have 6W = W + 250 => 5W = 250 => W = 50
Now, substitute W = 50 into equations (1) and (2) to find M and C:
- M = 50 + 250 = 300
- C = 2(50) = 100
Finally, we add up the numbers of men, women, and children:
Total = M + W + C = 300 + 50 + 100 = 450
So, there were 450 people at the football match.