A ticket booth sold 446 tickets and collected $3,188 in ticket sales. Adult tickets are $9.00 and children tickets are $2.00. How many adult tickets were sold?
9A+(446-A)2=3188 solve for A.
check my thinking.
To find the number of adult tickets sold, we can use a system of equations.
Let's represent the number of adult tickets sold as 'A' and the number of children tickets sold as 'C'.
There were a total of 446 tickets sold, so we can write the equation: A + C = 446
The total amount collected from adult tickets is found by multiplying the number of adult tickets (A) by the price of each adult ticket ($9.00), so the equation becomes: 9A
The total amount collected from children tickets is found by multiplying the number of children tickets (C) by the price of each children ticket ($2.00), so the equation becomes: 2C
The total amount collected from both types of tickets is $3,188, so we can write the equation: 9A + 2C = 3,188
Now we can solve these equations simultaneously to find the values of A and C.
A + C = 446 (Equation 1)
9A + 2C = 3,188 (Equation 2)
To make it easier to solve, let's multiply Equation 1 by -2, and then add it to Equation 2:
-2(A + C) = -2(446)
-2A - 2C = -892
This gives us:
-2A - 2C + 9A + 2C = -892 + 3,188
Simplifying the equation further, we get:
7A = 2,296
Now, divide both sides of the equation by 7 to solve for A:
A = 328
Therefore, 328 adult tickets were sold.