Question

A group of students were surveyed to find out their favorite subject in school. 1/6 chose history and 2/5 chose music. Of the students surveyed, 65 chose neither history nor music. How many students chose history and how many students chose music

Answer 1

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 = $\frac{1}{6}$ of (Total number of students) = $\frac{1}{6}\times \textrm{s}$ = $\frac{1}{6}\textrm{s}$

Number of students who chose history as favorite subject = $\mathbf{\frac{1}{6}s}$

Number of students who chose music as favorite subjects = $\frac{2}{5}$ of (Total number of students) = $\frac{2}{5}\times \textrm{s}$ = $\frac{2}{5}\textrm{s}$

Number of students who chose music as favorite subjects = $\mathbf{\frac{2}{5}s}$

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)

$\mathrm{s=\frac{1}{6}s+\frac{2}{5}s+65}$

$\mathrm{s=(\frac{1}{6}+\frac{2}{5})s+65}$

$\mathrm{s=(\frac{1\times5+2\times6}{30})s+65}$

$\mathrm{s=(\frac{17}{30})s+65}$

$\mathrm{s-\frac{17}{30}s=65}$

$\mathrm{(1-\frac{17}{30})s=65}$

$\mathrm{(\frac{1\times30-17}{30})s=65}$

$\mathrm{\frac{13}{30}s=65}$

$\mathrm{s=65\times\frac{30}{13}}$

$\mathrm{s=\frac{1950}{13}}$

$\therefore\mathbf{s=150}$

Number of students who chose history as favorite subject = $\frac{1}{6}\textrm{s}=\frac{1}{6}\times150=25$

Number of students who chose history as favorite subject = 25

Number of students who chose music as favorite subject = $\frac{2}{5}\textrm{s}=\frac{2}{5}\times150=60$

Number of students who chose music as favorite subject = 60