adult tickets for a play cost $5.50 and a child ticket cost $3.50. They sold 550 tickets and collected $2139.00. How many adult tickets sold

x-number the adult tickets

y-number the child tickets

x+y=550
5.50*x + 3.50*y =2139.00
----------
y=550-x
5.50*x +3.50*(550-x) =2139.00
-----
5.50*x +3.5*550- 3.50*x =2139.00
(5.5-3.5)*x +1925.00 = 2139.00
2*x=2139.00-1925.00
2*x=214
x=214/2
x=107
107 adult ticket were sold

To find the number of adult tickets sold, we can set up a system of equations.

Let's assume the number of adult tickets sold is A, and the number of child tickets sold is C.

According to the problem, the cost of an adult ticket is $5.50, so the total revenue from adult tickets would be 5.50 * A. Similarly, the revenue from child tickets would be 3.50 * C.

We also know that the total number of tickets sold is 550, so we can express this as the sum of adult and child tickets: A + C = 550.

Additionally, we're given the total revenue collected, which is $2139.00: 5.50A + 3.50C = 2139.00.

Now we have a system of two equations:

A + C = 550 (Equation 1)
5.50A + 3.50C = 2139.00 (Equation 2)

We can solve this system of equations to find the value of A.

One way to solve this system is by substitution:

From Equation 1, we can express C in terms of A: C = 550 - A.

Substitute this value of C into Equation 2:

5.50A + 3.50(550 - A) = 2139.00.

Now, simplify and solve for A:

5.50A + 1925 - 3.50A = 2139.00
2A + 1925 = 2139.00
2A = 2139.00 - 1925
2A = 214.00
A = 214.00 / 2
A = 107

Therefore, the number of adult tickets sold is 107.