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student tickets to the school musical cost $3 each. All other tickets cost $5 each. Suppose that 272 tickets were sold for a total of $1120. How many tickets of each type were sold?

  • math -

    first we represent unknowns with variables.
    let x = number of $3-tickets
    since the total number of tickets ($3 and $5) is equal to 272,
    let 272-x = number of $5-tickets
    then we set-up the equation. to get the total cost, we multiply each price of the ticket with their number. thus,
    3x + 5(272-x) = 1120
    3x + 1360 - 5x = 1120
    3x - 5x = 1120 - 1360
    -2x = -240
    x = 120 (number of $3-tickets)
    272-x = 152 (number of $5-tickets)

    hope this helps~ :)

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