A+S+C=120
12A+10S+6C=1100
A=C
2A+S=120
18A+10S=1100
multipuly top equation by 10, then subtract..
2A=100
A=50
C=50
S=20
12A+10S+6C=1100
A=C
2A+S=120
18A+10S=1100
multipuly top equation by 10, then subtract..
2A=100
A=50
C=50
S=20
Let's assume the number of adult tickets sold is A.
Since the number of adult tickets sold is equal to the number of child tickets sold, the number of child tickets sold is also A.
The number of senior tickets sold is S.
Given:
Total number of tickets sold = 120
Number of adult tickets sold + Number of senior tickets sold + Number of child tickets sold = Total number of tickets sold
So we have the equation:
A + S + A = 120
2A + S = 120
The cost of adult tickets = $12 each
The cost of senior tickets = $10 each
The cost of child tickets = $6 each
Given:
Total revenue from ticket sales = $1100
Revenue from adult ticket sales + Revenue from senior ticket sales + Revenue from child ticket sales = Total revenue
So we have the equation:
12A + 10S + 6A = 1100
18A + 10S = 1100
Now, we have a system of equations:
Equation 1: 2A + S = 120
Equation 2: 18A + 10S = 1100
We can solve this system of equations to find the values of A and S.
Multiplying Equation 1 by 10, we get:
10(2A + S) = 10(120)
20A + 10S = 1200
Subtracting this from Equation 2, we eliminate S:
(18A + 10S) - (20A + 10S) = 1100 - 1200
18A + 10S - 20A - 10S = -100
-2A = -100
A = 50
Substituting the value of A back into Equation 1, we can find S:
2A + S = 120
2(50) + S = 120
100 + S = 120
S = 20
Therefore, the number of senior tickets sold is 20.