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Explanation:
x = number of boys
The ratio of girls to boys is 4:1, meaning there are 4 times as many girls compared to boys. For example, the concert may have 40 girls and 10 boys.
For now, x is some unknown positive whole number. But we can say that 4x represents the number of girls, as we multiply by 4.
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We're told there are 75 more girls than boys, so,
number of girls = (number of boys) + 75
4x = x + 75
4x-x = 75
3x = 75
x = 75/3
x = 25
There are 25 boys and 4x = 4*25 = 100 girls.
We can see that 100-25 = 75 to show that there are 75 more girls compared to boys.
And also, the ratio 100:25 reduces fully to 4:1 after dividing both parts by the GCF 25. These two facts fully confirm the answers.
