Exactly 120 tickets were sold for a concert. The tickets cost $12 each for adults, $10 each for seniors, and $6 each for children. The number of adult tickets sold was equal to the number of child tickets sold. Given that the total revenue from the tickets sales was $1100, the number of senior tickets sold was?

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

why do you multiply the equation? and how do you know that 2Ax100= 100???

10*

To find the number of senior tickets sold, we can use algebraic equations and the given information.

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.