The ticket prices for a movie are shown in the illustration. Receipts for one showing were $1,930 for an audience of 205 people. How many general admission tickets and how many senior citizen tickets were sold?
not knowing the prices is a bit of a hindrance. However, if the prices were x and y, and there were s seniors, then
sx + y(205-s) = 1930
So, plug in your values for the ticket prices, and solve for s.
To determine the number of general admission and senior citizen tickets sold, we can set up a system of equations based on the given information. Let's denote the number of general admission tickets as "G" and the number of senior citizen tickets as "S".
From the illustration, we know the ticket prices are as follows:
- General admission tickets cost $12 each, so the total revenue from general admission tickets is 12 * G.
- Senior citizen tickets cost $8 each, so the total revenue from senior citizen tickets is 8 * S.
We also know that the total receipts for the showing were $1,930, which means the total revenue from both general admission and senior citizen tickets should add up to that amount.
So, we can set up the following equations:
12G + 8S = 1,930 (Equation 1) -- representing the revenue equation
G + S = 205 (Equation 2) -- representing the total number of tickets equation
To solve this system of equations, we can use substitution or elimination methods.
Let's use the substitution method:
1. Solve Equation 2 for one variable (G or S) in terms of the other variable.
G = 205 - S
2. Substitute the value of G from step 1 into Equation 1.
12(205 - S) + 8S = 1,930
3. Simplify and solve for S.
2,460 - 12S + 8S = 1,930
-4S = -530
S = 530/4
S = 132.5
Since ticket quantities must be whole numbers, we can conclude that 132 senior citizen tickets were sold.
4. Substitute the value of S into Equation 2 to find G.
G + 132 = 205
G = 205 - 132
G = 73
Therefore, 73 general admission tickets were sold.
In summary, 73 general admission tickets and 132 senior citizen tickets were sold for that showing.