Question

For a particular event, 340 tickets were sold for a total of $7600. If students paid $10 per ticket and nonstudents paid $40 per ticket, how many student tickets were sold?

Answer 1

We will solve it by equation method:

Let the number of students be x

Let the number of nonstudents be y.

Thus, 1st equation will be,

340 tickets were sold; 340 tickets comprises of students tickets & non students tickets

thus,

x + y = 340

y = 340 - x

2nd equation will be,

340 tickets were sold for a total of $7600 , Students (x) paid $10 per ticket and nonstudents (y) paid $40 per ticket

Thus,

( x * $ 10 ) + ( y * $ 40 ) = $ 7,600

$ 10x + $ 40y = $ 7,600

let's put y value as per equation 1 in above equation as follows:

$ 10x + $ 40 (340 -x) = $ 7,600

$ 10x + $ 13,600 - $ 40x = $ 7,600

$ 13,600 - $ 7,600 = $ 40x - $ 10x

$ 6,000 = $ 30x

x = $ 6,000 / $ 30

x = 200

Thus, 200 students (x) tickets sold.

We can also calculate non students tickets as follows

let's put x value in equation 1 is as follows:

y = 340 - x

y = 340 - 200

y = 140

Thus,

140 nonstudents (y) tickets sold.

Note:

We can cross check our answer:

( x * $ 10 ) + ( y * $ 40 ) = $ 7,600

( 200 * $ 10 ) + ( 140 * $ 40 ) = $ 7,600

$ 2000 + $ 5,600 = $ 7,600

$ 7,600 = $ 7,600