There were a total of 2000 tickets sold at a recent sporting event on Saturday. The cost of an adult ticket was $4.00 and a child's ticket was $2.00. The total amount of money collected was $6400.00. How many adult and child tickets were sold at the game?

A = # adult tickets

C = # child tickets
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A+C = 2000
4A + 2C = 6400

Solve the two equations simultaneously for A and C.

To find the number of adult and child tickets sold at the game, let's set up a system of equations to represent the given information.

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

From the given information, we have two equations:

1) A + C = 2000 (total number of tickets sold)
2) 4A + 2C = 6400 (total amount of money collected)

To solve these equations, we can use the substitution method or the elimination method. Let's use the substitution method.

From equation 1), we can isolate A:
A = 2000 - C

Now we substitute the value of A in equation 2):
4(2000 - C) + 2C = 6400

Simplifying the equation:
8000 - 4C + 2C = 6400
-2C = 6400 - 8000
-2C = -1600
C = -1600 / -2
C = 800

Now, substitute the value of C back into equation 1):
A + 800 = 2000
A = 2000 - 800
A = 1200

Therefore, 1200 adult tickets and 800 child tickets were sold at the game.