Respuesta :
Answer:
Number of students who chose history as favorite subject = 25
Number of students who chose music as favorite subject = 60
Step-by-step explanation:
Let the total number of students be 's'.
Number of students who chose history as favorite subject = [tex]\frac{1}{6}[/tex] of (Total number of students) = [tex]\frac{1}{6}\times \textrm{s}[/tex] = [tex]\frac{1}{6}\textrm{s}[/tex]
Number of students who chose history as favorite subject = [tex]\mathbf{\frac{1}{6}s}[/tex]
Number of students who chose music as favorite subjects = [tex]\frac{2}{5}[/tex] of (Total number of students) = [tex]\frac{2}{5}\times \textrm{s}[/tex] = [tex]\frac{2}{5}\textrm{s}[/tex]
Number of students who chose music as favorite subjects = [tex]\mathbf{\frac{2}{5}s}[/tex]
Number of students who chose neither history nor music as favorite subject = 65
Total number of students = (Number of students who chose history as favorite subject) + (Number of students who chose music as favorite subject) + (Number of students who chose neither history nor music as favorite subject)
[tex]\mathrm{s=\frac{1}{6}s+\frac{2}{5}s+65}[/tex]
[tex]\mathrm{s=(\frac{1}{6}+\frac{2}{5})s+65}[/tex]
[tex]\mathrm{s=(\frac{1\times5+2\times6}{30})s+65}[/tex]
[tex]\mathrm{s=(\frac{17}{30})s+65}[/tex]
[tex]\mathrm{s-\frac{17}{30}s=65}[/tex]
[tex]\mathrm{(1-\frac{17}{30})s=65}[/tex]
[tex]\mathrm{(\frac{1\times30-17}{30})s=65}[/tex]
[tex]\mathrm{\frac{13}{30}s=65}[/tex]
[tex]\mathrm{s=65\times\frac{30}{13}}[/tex]
[tex]\mathrm{s=\frac{1950}{13}}[/tex]
[tex]\therefore\mathbf{s=150}[/tex]
Number of students who chose history as favorite subject = [tex]\frac{1}{6}\textrm{s}=\frac{1}{6}\times150=25[/tex]
Number of students who chose history as favorite subject = 25
Number of students who chose music as favorite subject = [tex]\frac{2}{5}\textrm{s}=\frac{2}{5}\times150=60[/tex]
Number of students who chose music as favorite subject = 60
