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WITCHER [35]
2 years ago
13

At a birthday party there were five more girls than boys. If the ratio of girls to boys was 4 to 3,

Mathematics
1 answer:
exis [7]2 years ago
3 0

Let number if boys be x

  • No of girls=x+5

ATQ

\\ \sf\longmapsto \dfrac{x+5}{x}=\dfrac{4}{3}

\\ \sf\longmapsto 3(x+5)=4x

\\ \sf\longmapsto 3x+15=4x

\\ \sf\longmapsto 4x-3x=15

\\ \sf\longmapsto x=15

<h3>Number of girls</h3>

\\ \sf\longmapsto x+5=15+5=20

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In a group of Explore students, 38 enjoy video games, 12 enjoy going to the movies and 24 enjoy solving mathematical problems. O
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Here we have;

n(A∪B∪C) = n(A) + n(B) + n(C) - n(A∩B) - n(B∩C) -n(A∩C) + n(A∩B∩C)

= 38 + 12 + 24 - n(A∩B) - n(B∩C) -n(A∩C) + 8

Also the number of student that like only one activity is found from the following equation;

n(A) - n(A∩B) - n(A∩C) + n(A∩B∩C) + n(B) - n(A∩B) - n(B∩C) + n(A∩B∩C) + n(C) - n(C∩B) - n(A∩C) + n(A∩B∩C) = 30

n(A) + n(B) + n(C) - 2·n(A∩B) - 2·n(A∩C) - 2·n(B∩C) + 3·n(A∩B∩C) = 30

38 + 12 + 24 - 2·n(A∩B) - 2·n(A∩C) - 2·n(B∩C) + 24 = 30

- 2·n(A∩B) - 2·n(A∩C) - 2·n(B∩C) = -68

n(A∩B) + n(B∩C) + n(A∩C) = 34

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