Respuesta :
Answer:
210 soccer and 30 enjoying basketball
Step-by-step explanation:
Given: for every three boys who enjoyed soccer five boys enjoyed basketball. The girl's survey had a ratio of the number of girls who enjoy soccer to the number of girls who enjoy basketball of 7:1
To Find: If the same number of boys and girls were surveyed, 90 boys enjoy soccer how many girls enjoying each sport
Solution: For every 3 boys enjoying soccer = 5 boys enjoying basketball
ratio of boys enjoying soccer and basketball = [tex]3:5[/tex]
ratio of girls enjoying soccer and basketball = [tex]7:1[/tex]
Now,
let total number of boys enjoying sports = [tex]\text{b}[/tex]
let total number of girls enjoying sports = [tex]\text{g}[/tex]
Number of boys enjoying soccer = [tex]\frac{3}{8}\text{b}[/tex]
it is given that,
[tex]\frac{3}{8}\text{b}[/tex] = [tex]90[/tex]
total number of boys [tex]\text{b}[/tex] =[tex]\frac{8}{3}\times90[/tex]
= [tex]240[/tex]
total number of girls enjoying sports = total number of boys enjoying �� sports
total number of girls enjoying sports = [tex]240[/tex]
number of girls enjoying soccer = [tex]\frac{7}{8}\text{g}[/tex]
= [tex]\frac{7}{8}\times240[/tex]
= [tex]210[/tex]
number of girls enjoying basketball = [tex]\frac{1}{8}\times{g}[/tex]
= [tex]\frac{1}{8}\times240[/tex]
= [tex]30[/tex]
number of girls enjoying soccer is [tex]210[/tex] and number of girls enjoying basketball is [tex]30[/tex]
Using proportions, it is found that:
- 210 girls enjoy soccer.
- 30 girls enjoy basketball.
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- For every 3 boys that enjoyed soccer, 5 enjoyed basketball. Thus, [tex]\frac{3}{3 + 5} = \frac{3}{8}[/tex] of the boys enjoyed soccer, and [tex]\frac{5}{8}[/tex] enjoyed basketball.
- 90 boys enjoy soccer, which is 3/8 of the total number of boys. Thus:
[tex]\frac{3b}{8} = 90[/tex]
[tex]3b = 720[/tex]
[tex]b = \frac{720}{3}[/tex]
[tex]b = 240[/tex]
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- There are 240 boys.
- The number of girls is also the same, 240.
- The soccer:basketball ratio for girls means that [tex]\frac{7}{8}[/tex] of them enjoy soccer and [tex]\frac{1}{8}[/tex] basketball, thus:
[tex]\frac{7}[8}240 = \frac{7 \times 240}{8} = 7 \times 30 = 210[/tex]
[tex]\frac{1}[8}240 = \frac{1 \times 240}{8} = 1 \times 30 = 30[/tex]
- 210 girls enjoy soccer.
- 30 girls enjoy basketball.
A similar problem is given at https://brainly.com/question/17245640
