Question

1500 concert tickets were sold $25 for covered pavilion seats and $15 for lawn seats total amount made $28,500

Answer 1

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.

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;

`x+y=1500 \ \ \ \ equation \ 1`

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.

`25x+15y = 28500`

Dividing by 5 on both side we get;

`5x+3y= 5700 \ \ \ \ equation \ 2`

Now Multiplying equation by 3 we get;

`3(x+y)=1500*3\\3x+3y = 4500 \ \ \ \ equation \ 3`

Now Subtracting equation 3 from 2 we get;

`(5x+3y)-(3x+3y)=5700-4500\\5x+3y-3x-3y=1200\\2x=1200\\x=(1200)/(2)=600`

Substituting the value of x in equation 1 we get;

`x+y=1500\\600+y=1500\\y=1500-600\\y=900`

Hence Number of Pavilion seat is 600 and number of lawn seats is 900.