SOLUTION: the ratio of the number of boys to the number of girls in a school hall was 8:3 at first. Then 45 more girls joined the students in the hall and there was an equal number of boys a

Question 1190436: the ratio of the number of boys to the number of girls in a school hall was 8:3 at first. Then 45 more girls joined the students in the hall and there was an equal number of boys and girls. How many children were in the hall in the end?
Found 2 solutions by josgarithmetic, math_tutor2020:
Answer by josgarithmetic(39625) (Show Source): You can put this solution on YOUR website!
8p boys and 3p girls initially

3p+45 girls next and ratio of boys and girls is equal.

.
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Answer by math_tutor2020(3817) (Show Source): You can put this solution on YOUR website!

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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