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Answer:
The system of equation form is [tex]x+y=500[/tex] and [tex]5x+8y=3400[/tex]
Student tickets sold is 200 and Adult tickets sold is 300.
Step-by-step explanation:
Given : Searches related to A 500-seat theater charges $5 per ticket for students and $8 per ticket for adults. All seats for the performance tonight are filled and total ticket sales are $3400.
To find : The system of equation form to determine how many student tickets and how many adult tickets were sold.
Solution :
Let x = the number of student tickets sold.
Let y = the number of adult tickets sold.
A 500-seat theater charges $5 per ticket for students and $8 per ticket for adults. Total ticket sales are $3400.
[tex]x+y=500[/tex] ........[1]
[tex]5x+8y=3400[/tex] .......[2]
The system of equation form is [tex]x+y=500[/tex] and [tex]5x+8y=3400[/tex]
Now, we solve the system of equations
Substitute x=500-y from [1] in [2]
[tex]5x+8y=3400[/tex]
[tex]5(500-y)+8y=3400[/tex]
[tex]2500-5y+8y=3400[/tex]
[tex]3y=900[/tex]
[tex]y=300[/tex]
Put back in equation [1]
[tex]x+300=500[/tex]
[tex]x=200[/tex]
Therefore, Student tickets sold is 200 and Adult tickets sold is 300.
Answer:
Number of tickets sold to students and adults are 200 and 300 respectively.
Step-by-step explanation:
Let, the number of student tickets = x and number of adult tickets = y.
As, there are total number of 500 seats in the theater, we have,
[tex]x+y=500[/tex]
Also, the price of the tickets is $5 per student and $8 per adult.
Since, the total sales are of $3400. We get,
[tex]5x+8y=3400[/tex]
So, the system of equations is given by,
x+y=500 ........................... (1)
5x+8y=3400 ..........................(2)
Multiply equation (1) by 5 and subtract with equation (2), we get,
3y = 900 i.e. y= 300
So, x=500-y implies x=500-300 i.e. x= 200
Hence, the number of tickets sold to students and adults are 200 and 300 respectively.
