Question

Students surveyed boys and girls separately to determine which sport was enjoyed the most. After completing the boy survey, it was determined that for every 3 boys who enjoyed soccer, 5 boys enjoyed basketball. The girl survey had a ratio of the number of girls who enjoyed soccer to the number of girls who enjoyed basketball of 7: 1. If the same number of boys and girls were surveyed, and 90 boys enjoy soccer, how many girls enjoy each sport?

Answer 1

Ratio of boys who liked soccer to boys who liked basketball = 3:5

Given :-

Number of boys who enjoyed soccer :-

`\color{hotpink} = \color{hotpink}90 \: \: \color{hotpink}boys`

Total number of boys who were surveyed were equal to the total number of girls who were surveyed .

Which means :-

Let the total number of boys who were surveyed be x .

Total number of boys =

`= (3)/(8) * x = 90`

`= x = 90 / (3)/(8)`

`= x = 90 * (8)/(3)`

`= x = (720)/(3)`

`\color{hotpink}x =\color{hotpink} 240`

Which means a total of 240 boys were surveyed .

Number of boys who liked basketball :-

`= (5)/(8) * 240`

`= (1200)/(8)`

`\color{hotpink} = 150 \: \: boys`

Which means a total of 150 boys liked basketball .

Number of girls who liked soccer :-

`= (7)/(8) * 240`

`= (1680)/(8)`

`\color{hotpink} = 210 \: \: girls`

A total of 210 girls enjoyed soccer .

Number of girls who enjoyed basketball :-

`= (1)/(8) * 240`

`= (240)/(8)`

`\color{hotpink} = 30 \: \: girls`

A total of 30 girls like basketball .

Therefore , 210 girls enjoyed soccer and 30 girls enjoyed basketball .