A total of 900 tickets were sold for a game for a total of $1,775.00. If adult tickets sold for $2.50 and children's tickets sold for $1.50, how many of each kind of tickets were sold?
see related questions below, or the mixture problems posted after this one.
To solve this problem, let's assume the number of adult tickets sold as 'A' and the number of children's tickets sold as 'C'.
We know two conditions: the total number of tickets sold is 900 and the total amount collected is $1,775.
So, we can set up two equations based on these conditions:
1. A + C = 900 (equation 1)
2. (2.50)A + (1.50)C = 1775 (equation 2)
To solve this system of equations, we can use the method of substitution or elimination.
Let's use the method of substitution:
From equation 1, we know A = 900 - C.
Substitute this value of A in equation 2:
(2.50)(900 - C) + (1.50)C = 1775.
Expanding and simplifying:
2250 - 2.50C + 1.50C = 1775.
Combine like terms:
-1.00C = 1775 - 2250.
Simplifying again:
-1.00C = -475.
Dividing by -1.00:
C = 475.
Now, substitute the value of C in equation 1 to find A:
A + 475 = 900.
A = 900 - 475.
A = 425.
Therefore, 425 adult tickets and 475 children's tickets were sold.