A concert promoter needs to make $68,400 from the sale of 1880 tickets. The promoter charges $30 for some tickets and $50 for the others. Let x represent the number of $30 tickets and y represent the number of $50 tickets. (a) Write an equation that states that the sum of the tickets sold is 1880. (b) Write a formula for how much money is received from the sale of $30 tickets? $ (c) Write a formula for how much money is received from the sale of $50 tickets? $ (d) Write an equation that states that the total amount received from the sale is $68,400. (e) Solve the equations simultaneously to find how many tickets of each type must be sold to yield the $68,400. x = 38400 y = 30000

1280 of the $30 tickets and 600 of the $50 tickets

Explanation:

If x represents the number of $30 tickets and y represents the number if %50 tickets then:

(a) the sum of the tickets sold is 1880 = x + y

(b) how much money is received from the sale of $30 tickets = 30x

(c) how much money is received from the sale of $50 tickets = 50y

(d) the total amount received from the sale is $68,400 = 30x + 50y = $68,400

(e) Solving the simultaneous equations, if 1880 = x + y, then x = 1880 - y. Substitute this in total amount received equation and solve for y i. e. 30 (1880 - y) + 50y = $68,400

56,400 - 30y + 50y = $68,400

20y = 12,000

y = 600 tickets (we have to sell 600 of the $50 tickets)

Step 2. Substitute the y figure to get the x amount i. e. 30x + 50 (600) = $68,400

30x + 30,000 = $68,400

30x = $38,400

x = 1280 tickets (we have to sell 1280 of the $30 tickets)