Answer:
71 adult tickets, 135 child tickets
Step-by-step explanation:
[tex]\textcolor{steelblue}{\text{\textcircled{1} Define the variables}}[/tex]
Let the number of adult and child tickets sold be a and c respectively.
[tex]\textcolor{steelblue}{\text{\textcircled{2} Form and label 2 equations}}[/tex]
Adult tickets +child tickets= total number of tickets sold
a +c= 206 -----(1)
Revenue from child tickets +revenue from adult tickets= total revenue
Revenue from child tickets
= number of child tickets sold ×cost of each ticket
= 2.65c
Revenue from adult tickets
= number of adult tickets sold ×cost of each adult ticket
= 5.70a
2.65c +5.70a= 762.45 -----(2)
[tex]\textcolor{steelblue}{\text{\textcircled{3} Solve by substitution}}[/tex]
From (1):
a= 206 -c -----(3)
Substitute (3) into (2):
2.65c +5.70(206 -c)= 762.45
Expand:
2.65c +1174.2 -5.70c= 762.45
Simplify:
-3.05c +1174.2= 762.45
-3.05c= 762.45 -1174.2
-3.05c= -411.75
c= -411.74 ÷(-3.05)
c= 135
Substitute c= 135 into (3):
a= 206 -135
a= 71
[tex]\textcolor{steelblue}{\text{\textcircled{4} Concluding statement}}[/tex]
Thus, 71 adult tickets and 135 child tickets were sold.
