A = # adult tickets
C = # child tickets
-----------------
A+C = 2000
4A + 2C = 6400
Solve the two equations simultaneously for A and C.
C = # child tickets
-----------------
A+C = 2000
4A + 2C = 6400
Solve the two equations simultaneously for A and C.
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.