At a fun fair, each mother there had brought 2 children. At the end of the day, it was found that 36 mothers had lost one or both of their children and 62 children had lost their mothers. How many mothers lost only one of their children and how many mothers lost both of their children?
Assuming each child has only one mother.
Let m be the number of mothers who lost both children.
Let n be the number who lost only one child.
36 mothers had lost one or both of their children:
(1)... m + n = 36
62 children had lost their mothers:
(2)... 2m + n = 62
Solve for n and m.
Let's represent the number of mothers who lost only one child as 'x' and the number of mothers who lost both children as 'y'.
We know that each mother had brought 2 children, so the total number of children at the fun fair is 36 * 2 = 72.
From the given information, we can form the following equations:
x + y = 36 (equation 1, as there are 36 mothers who lost one or both of their children)
2x + 2y = 62 (equation 2, as there are 62 children who lost their mothers)
We can solve these equations to find the values of 'x' and 'y'.
Dividing equation 2 by 2, we get:
x + y = 31 (equation 3)
Subtracting equation 3 from equation 1, we get:
36 - 31 = 5
So, y = 5.
Substituting the value of y in equation 3, we get:
x + 5 = 31
x = 31 - 5
x = 26
Therefore, 26 mothers lost only one of their children and 5 mothers lost both of their children.
To solve this problem, let's break it down step by step.
Let's assign variables to the unknowns:
Let M represent the number of mothers.
Let C represent the number of children.
From the given information, we can deduce the following equations:
1) Each mother brought 2 children, so the total number of children is 2 times the number of mothers: C = 2M.
2) It was found that 36 mothers had lost one or both of their children. This means that there are 36 mothers who lost at least one child: M - 36.
3) It was also found that 62 children had lost their mothers. Since each mother brought 2 children, the number of children who lost their mothers is 2 times the number of mothers: 2M - 62.
Now we can solve the equations.
From equation 1:
C = 2M.
Plug this into equation 3:
2M - 62 = 2M. (Since C = 2M)
Simplify:
-62 = 0.
This equation doesn't make sense because it leads to a contradiction. Therefore, there is no unique solution to this problem. It appears that there might be an error or inconsistency in the given information.