At the movie theater, child admission is $5.30 and adult admission is $9.50. On Tuesday, 158 tickets were sold for a total sales of $1198.60. How many adult tickets were sold that day?
If a adult tickets were sold, then the rest (158-a) were child tickets. SO now just add up the sales and solve for a.
9.50a + 5.30(158-a) = 1198.60
To find the number of adult tickets sold, we need to set up a system of equations.
Let's assume the number of child tickets sold is C, and the number of adult tickets sold is A.
From the information given, we can set up the following equations:
1) C + A = 158 (equation 1, representing the total number of tickets sold)
2) 5.30C + 9.50A = 1198.60 (equation 2, representing the total sales amount)
To solve this system of equations, we will use the method of substitution.
From equation 1, we can isolate one of the variables. Let's solve for C in terms of A:
C = 158 - A
Now, substitute this expression for C in equation 2:
5.30(158 - A) + 9.50A = 1198.60
Now, simplify the equation:
837.4 - 5.30A + 9.50A = 1198.60
4.20A = 1198.60 - 837.4
4.20A = 361.20
Divide both sides of the equation by 4.20 to solve for A:
A = 361.20 / 4.20
A ≈ 86
Therefore, approximately 86 adult tickets were sold that day.