At the movie theatre, child admission is 5.50 and adult admission is 8.90. On Tuesday, 150 tickets were sold for a total sales of 1051.80. How many child tickets were sold that day?
a + c = 150
8.9a + 5.5c = 1051.80
I would change the first equation to c = 150-a , and use substitution.
I just did that and , unless I made an error, I did not get a whole number
as I must.
Let's say the number of child tickets sold is "C" and the number of adult tickets sold is "A".
According to the given information:
1. Child admission is $5.50, so the total revenue from child tickets is 5.5* C = 5.5C.
2. Adult admission is $8.90, so the total revenue from adult tickets is 8.9 * A = 8.9A.
3. The total number of tickets sold is given by C + A = 150.
4. The total revenue from all the tickets sold is $1051.80, so 5.5C + 8.9A = 1051.80.
We have a system of two equations with two variables that we can solve simultaneously to find the values of C and A.
Using the substitution method, we can rewrite equation 3 as C = 150 - A.
Substituting this expression for C in equation 4, we get:
5.5(150 - A) + 8.9A = 1051.80.
Expanding the equation:
825 - 5.5A + 8.9A = 1051.80.
Combining like terms:
825 + 3.4A = 1051.80.
Subtracting 825 from both sides of the equation:
3.4A = 226.80.
Dividing both sides by 3.4:
A = 226.80 / 3.4 = 66.
Therefore, there were 66 adult tickets sold.
Now, substituting this value of A into equation 3 to find C:
C = 150 - A = 150 - 66 = 84.
Therefore, there were 84 child tickets sold.
To solve this problem, we can use a system of equations. Let's define two variables:
- Let C be the number of child tickets sold.
- Let A be the number of adult tickets sold.
We can create two equations based on the given information:
1. The total number of tickets sold: C + A = 150
2. The total sales amount: 5.50C + 8.90A = 1051.80
Now, we can use these equations to find the values of C and A.
First, let's solve equation 1 for one variable:
C = 150 - A
Now, substitute this value of C into equation 2:
5.50(150 - A) + 8.90A = 1051.80
Now we can solve this equation to find the value of A (adult tickets sold). After that, we can substitute this value of A back into equation 1 to find the value of C (child tickets sold).