Given:
Entry ticket for students = $5
Entry ticket for adults = $5 + $4 = $9
Number of people = 600
Total amount collected = $3500
Let's find the number of students and adults who visited on that day.
Let S represent the number of students and A represent the number of adults.
We hav the system of equations:
5S + 9A = 3500
S + A = 600
Let's solve the system of equations simultaneously using substitution method.
Rewrite the second equation for S:
S = 600 - A
Substitute (600 - A) for S in the first equation:
[tex]\begin{gathered} 5(600\text{ - A\rparen + 9A}=\text{ 3500} \\ \\ \text{ Apply distributive property:} \\ 5(600)+5(-A)+9A=3500 \\ \\ 3000-5A+9A=3500 \\ \\ 3000+4A=3500 \\ \\ 4A=3500-3000 \\ \\ 4A=500 \end{gathered}[/tex]Divide both sides by 4:
[tex]\begin{gathered} \frac{4A}{4}=\frac{500}{4} \\ \\ A=125 \end{gathered}[/tex]Substitute 125 for A in either of the equations:
[tex]\begin{gathered} S=600-A \\ \\ S=600-125 \\ \\ S=475 \end{gathered}[/tex]Therefore, we have the solutions:
S = 475, A = 125
Therefore, the number of students that visited is 475 while the number of adults is 125 .
ANSWER:
Students = 475; Adults = 125
