Question 1190436
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The ratio 8:3 means we have 8 boys for every 3 girls
It scales up to 8x:3x for some positive whole number x.


8x = number of boys
3x = number of girls


Now we add 45 more girls to get 3x+45 girls overall
We have an equal amount of both genders, so
8x = 3x+45
8x-3x = 45
5x = 45
x = 45/5
x = 9


This leads to
8x = 8*9 = 72 boys
3x = 3*9 = 27 girls
before the extra 45 girls enter the hall


The ratio 72:27 reduces to 8:3 when you divide both parts by the GCF 9. This helps confirm we have the correct values.


Now add 45 to the 27 initial group of girls
27+45 = 72
This further helps confirm the correct values earlier.


Therefore, there are 72+72 = 144 students



Answer: 144
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