A concert promoter must sell 1820 tickets for an upcoming concert. They can sell discount tickets for $40 each, and premium tickets for $45 each, but the total sales must equal $76,300. Let x be the number of discount tickets sold, and y be the number of premium tickets sold. Set up, and solve, the system of equations to find the number of tickets of each type sold.

Give your answer in the form (x, y)

You want the number of discount (x) and premium (y) tickets to be sold so that a total of 1820 tickets are sold for $40 and $45, respectively, and they generate revenue of $76,300.

Equations

The equations reflect the relationships stated in the problem:

x + y = 1820 . . . . . . the total number of tickets sold is 1820

40x +45y = 76,300 . . . . . total sales must be $76,300

Solution

It usually works well to substitute for the variable representing the lower-price tickets:

40(1820 -y) +45y = 76300 . . . . . . substitute for x using the first equation

5y = 3500 . . . . . . . . . . . . . . subtract 72800, simplify

y = 700 . . . . . . . . . . . . divide by 5

x = 1820 -700 = 1120

The numbers of tickets of each type sold are (x, y) = (1120, 700).