Respuesta :
Question is Incomplete, Complete question is given below.
One evening 1500 concert tickets were sold for the Jazz Fest. Tickets cost $25 for covered pavilion seats and $15 for lawn seat. Total receipts were $28,500. How many of each type of ticket were sold?
Answer:
Number of Pavilion seat is 600 and number of lawn seats is 900.
Step-by-step explanation:
Given:
Total Number of ticket sold = 1500
Let number of Pavilion seat be x.
Let number of lawn seats be y.
hence the equation can be framed as;
[tex]x+y=1500 \ \ \ \ equation \ 1[/tex]
Also Given
Total Amount made = $28,500
Cost of pavilion seat = $25
Cost of lawn seat = $15
Total Amount made is equal to Cost of pavilion seat multiplied by number of Pavilion seat plus Cost of lawn seat multiplied by number of lawn seats.
[tex]25x+15y = 28500[/tex]
Dividing by 5 on both side we get;
[tex]5x+3y= 5700 \ \ \ \ equation \ 2[/tex]
Now Multiplying equation by 3 we get;
[tex]3(x+y)=1500\times3\\3x+3y = 4500 \ \ \ \ equation \ 3[/tex]
Now Subtracting equation 3 from 2 we get;
[tex](5x+3y)-(3x+3y)=5700-4500\\5x+3y-3x-3y=1200\\2x=1200\\x=\frac{1200}{2}=600[/tex]
Substituting the value of x in equation 1 we get;
[tex]x+y=1500\\600+y=1500\\y=1500-600\\y=900[/tex]
Hence Number of Pavilion seat is 600 and number of lawn seats is 900.
