MHB How many boys and girls in a school hall

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There was an equal number of boys and girls in a school hall, initially denoted as B for boys and G for girls, where G equals B. After 108 boys left, the number of girls became four times the remaining boys. The calculations reveal that the initial number of boys was 144, leading to the same number of girls. Thus, the total number of pupils in the hall at first was 288. The problem illustrates a straightforward algebraic relationship between the number of boys and girls in the hall.
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There was an equal number of boys and girls in a school hall. After 108 boys left the hall, the number of girls in the hall became 4 times the number of boys in the hall. How many pupils were there in the hall at first?

my work:

Number of Boys = B
Number of Girls = G
G = B

We know that the number of girls was 4 times more after 108 boys left.

For boys:
-------------------------------------------------------
G = 4(b-108).
And since we know G = B

B = 4(B - 108)
B = 144.
------------------------------------------------------

For girls
-----------------------------------------------------
Then I plugged it back in G = 4(B - 108)

so, G = 4(144 - 108)
G = 4(36) = 144.
---------------------------------------------------

Total number of students is 144 + 144 = 288.
 
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Johnx said:
There was an equal number of boys and girls in a school hall. After 108 boys left the hall, the number of girls in the hall became 4 times the number of boys in the hall. How many pupils were there in the hall at first?
Correct! Good job...

Can be done quicker since B = G.
B - 108 = B / 4
4B - 432 = B
3B = 432
B = 144 : so 2B = 288
 
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