Answer :
The price of one senior citizen ticket is $5 and this can be determined by forming the linear equation in two variables.
Given :
- The school that Lisa goes to is selling tickets to the annual talent show.
- On the first day of ticket sales the school sold 20 senior citizen tickets and 40 student tickets for a total of $220.
- The school took in $250 on the second day by selling 20 senior citizen tickets and 50 student tickets.
Let the price of each senior citizen ticket be 'x' and the price of each student ticket be 'y'.
So, the linear equation that represents the total sales of day one is:
20x + 40y = 220
x + 2y = 11
x = 11 - 2y --- (1)
The linear equation that represents the total sales of day two is:
20x + 50y = 250
2x + 5y = 25 --- (2)
Now, substitute the value of 'x' in equation (2).
2(11 - 2y) + 5y = 25
Simplify the above expression.
22 - 4y + 5y = 25
y = $3
Now, substitute the value of 'y' in equation (1).
x = 11 - 2(3)
x = $5
So, the price of one senior citizen ticket is $5.
For more information, refer to the link given below:
https://brainly.com/question/11897796
Final answer:
By forming and solving a system of linear equations based on the information given for two days of ticket sales, we deduce that the price of one senior citizen ticket is $5.
Explanation:
The question involves setting up a system of linear equations based on the given information about ticket sales and total income from those sales to find the price of one senior citizen ticket. To start, we set up two equations based on the given data:
1. For the first day: 20S + 40C = $220
2. For the second day: 20S + 50C = $250
Where S represents the price of a senior citizen ticket, and C represents the price of a student ticket.
We can use the method of elimination or substitution to find the values of S and C. By subtracting the first equation from the second, we can eliminate S and solve for C. Once we have the value of C, we can substitute it into one of the equations to find the value of S.
By subtracting (1) from (2), we get:
10C = $30 ⇒ C = $3
Substituting C = $3 into equation (1), we have:
20S + 40(3) = $220 ⇒ 20S + $120 = $220 ⇒ 20S = $100 ⇒ S = $5
Hence, the price of one senior citizen ticket is $5.
