A moment ago, 80% of the children in a hall were girls. 48 girls and 2 boys left the hall. The remaining children were then told to form groups of 9. In each group, there were 2 boys. How many children were there in the hall first?

initially, b/g = 1/4

after some left, (b-2)/(g-48) = 2/7 since there were groups of 2 boys and 7 girls.

g=4b
7(b-2) = 2(4b-48)
b = 82
so g = 328

so, at first there were 410 children

after kids left, there were
80 boys
280 girls
making 40 groups of 2boys and 7girls

Dear Steve,

Thank you very much for your kind help.
Can understand clearly.

With regards,
Surya

Martha spent 4/a of her allowance on food and shopping.what fraction of her allowance had she

left

To find out how many children were in the hall initially, we can solve the problem step by step:

Let's assume the total number of children in the hall initially is represented by "x".

We are given that 80% of the children in the hall were girls. So, initially, there were 0.8x girls in the hall.

We are also given that 48 girls and 2 boys left the hall. Therefore, the number of girls remaining in the hall is 0.8x - 48.

We are told that the remaining children were then told to form groups of 9, and in each group, there were 2 boys. This means that the number of remaining children must be a multiple of 9 and that the number of remaining boys must be a multiple of 2.

Let's determine the number of remaining boys:
Since there were 2 boys leaving the hall, the number of remaining boys is x (initial number of boys) - 2.

Now, since the remaining boys must be a multiple of 2, we can represent the remaining number of boys as:
Number of remaining boys = 2k, where k is an integer.

Next, let's determine the total number of remaining children:
The number of remaining children is the sum of remaining girls and remaining boys:
Number of remaining children = (0.8x - 48) + (x - 2) = 1.8x - 50.

Since the remaining number of children must be a multiple of 9, we can represent the remaining number of children as:
Number of remaining children = 9n, where n is an integer.

Equating the two expressions for the number of remaining children, we have:
1.8x - 50 = 9n.

To simplify the equation, we can divide both sides by 1.8:
x - 27.78 = 5n.

From this equation, we see that x (the initial number of children) must be divisible by 5. So we can start by checking multiples of 5 until we find a number that satisfies all the given conditions.

Let's start by checking the first multiple of 5, which is 5 itself. Substituting x = 5 into the equation x - 27.78 = 5n, we get:
5 - 27.78 = 5n,
-22.78 = 5n,
This does not satisfy the equation since n is not an integer.

Let's try the next multiple of 5, which is 10. Substituting x = 10 into the equation, we get:
10 - 27.78 = 5n,
-17.78 = 5n,
Again, this does not satisfy the equation.

Continuing this process, we find that x = 35 is the first multiple of 5 that satisfies the equation:
35 - 27.78 = 5n,
7.22 = 5n.

Since n must be an integer, we can substitute n = 1 and validate if it satisfies all the conditions:
If n = 1, then x (initial number of children) = 35.

Hence, there were 35 children in the hall initially.