a ticket booth sold 456 tickets and collected $2311.50 in ticket sales. Adult tickets are $6.50 and child tickets are $2. how many tickets of each type were sole?
I'll try to help.
You know that a certain number of child tickets and a certain number of adult tickets must add up to equal 456.
Say x = adult tickets (number)
y = # child tickets
So x + y = 456
And the money collected is :
6.5x + 2y = 2311.5
2(x + y = 456) ==> 2x + 2y = 912.
6.5x + 2y = 2311.5
- (2x + 2y = 912)
4.5x = 1399.5
x = 1339.5 / 4.5 = 311
311 + y = 456
y = 145
SO # adult tickets = 311 # child tickets = 145
Hope that helped. Peace out.
Adult tickets --->
children tickets --> 456-x
6.5x + 2(456-x) = 2311.5
times 2
13x + 4(456-x) = 4623
9x = 2799
x = 311
so 311 adult tickets and 145 children tickets
To solve this problem, we can use a system of equations. Let's assign variables to the unknowns:
Let's say the number of adult tickets sold is A, and the number of child tickets sold is C.
From the given information, we can set up two equations based on the number of tickets and the total sales:
1) A + C = 456 (equation based on the number of tickets sold)
2) 6.50A + 2C = 2311.50 (equation based on the total sales)
Now, we can solve this system of equations to find the values of A and C.
First, let's solve equation 1) for A:
A = 456 - C
Substitute this value of A into equation 2):
6.50(456 - C) + 2C = 2311.50
Simplify the equation:
2964 - 6.50C + 2C = 2311.50
4.5C = 652.50
C = 145
Substitute this value of C back into equation 1) to find A:
A = 456 - 145
A = 311
Therefore, 311 adult tickets and 145 child tickets were sold.