Answer:
Adults = 167
Students = 256
Teachers = 85
Step-by-step explanation:
Let:
S represents Students
A represents Adults
T represents Teachers
From the instructions in the question, we have that:
[tex]A + S = 423[/tex] -- (1)
[tex]8A + 5S = 2616[/tex] -- (2)
Make A the subject in (1)
[tex]A + S = 423[/tex]
[tex]A = 423 - S[/tex]
Substitute [tex]423 - S[/tex] for A in (2)
[tex]8A + 5S = 2616[/tex]
[tex]8(423 - S) + 5S = 2616[/tex]
Open Bracket
[tex]3384 - 8S + 5S = 2616[/tex]
[tex]3384 -3S = 2616[/tex]
Solve for S
[tex]-3S = 2616 - 3384[/tex]
[tex]-3S = -768[/tex]
[tex]S = -768/-3[/tex]
[tex]S = 256[/tex]
Recall that [tex]A = 423 - S[/tex]
[tex]A = 423 - 256[/tex]
[tex]A = 167[/tex]
From the question, we understand that;
[tex]T = \frac{1}{3}S[/tex]
[tex]T = \frac{1}{3} * 256[/tex]
[tex]T = 85.333[/tex]
[tex]T = 85[/tex] (Approximated)
