ANSWER
• Science: 1080 students
,
• Social Studies: 720 students
,
• Reading: 360 students
,
• Math: 540 students
EXPLANATION
Assuming that each student can pick only one subject as their favorite, we can find the total number of students that were surveyed:
• Science: 30 students
,
• Social Studies: 20 students
,
• Reading: 10 students
,
• Math: 15 students
So,
[tex]30+20+10+15=75[/tex]
In total, 75 students were surveyed. Based on this survey, we have can conclude the proportion of students that have each subject as their favorite,
[tex]\begin{gathered} \begin{cases}Science:\frac{30}{75}=\frac{2}{5} \\ Social\text{ }studies:\frac{20}{75}=\frac{4}{15} \\ Reading:\frac{10}{75}=\frac{2}{15}\end{cases} \\ \begin{cases}Math:\frac{15}{75}=\frac{1}{5} \\ \end{cases} \end{gathered}[/tex]
If there are 2,700 students in the school, based on this survey, we can expect that the proportions will be the same,
[tex]Science:\frac{2}{5}\cdot2700=1080[/tex][tex]Social\text{ }studies:\frac{4}{15}\cdot2700=720[/tex][tex]Reading:\frac{2}{15}\cdot2700=360[/tex][tex]Math:\frac{1}{5}\cdot2700=540[/tex]
Hence, the number of expected students for each of the favorite subjects is:
• Science: 1080 students
,
• Social Studies: 720 students
,
• Reading: 360 students
,
• Math: 540 students
