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14 December, 13:31

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

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  1. 14 December, 13:45
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    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)
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