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    system of equations word problem

    Receipts for a concert, attended by 450 people, were $2775. If reserved-seat tickets were $7 and general-admission tickets were $4, how many of each type of ticket were sold?
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Patience View Post
    Receipts for a concert, attended by 450 people, were $2775. If reserved-seat tickets were $7 and general-admission tickets were $4, how many of each type of ticket were sold?
    This is another application of simultaneous equations.

    let the number of reserved tickets sold be r
    let the number of general admission tickets sold be g

    then the the money gained from selling reserved tickets is 7r and the money gained from selling general admission tickets is 4g. the total number of tickets sold is 450. so we have:

    r + g = 450 ..................(1)
    7r + 4g = 2775 .............(2)

    4r + 4g = 1800 ..............(3) = (1)*4
    7r + 4g = 2775 ..............(2)

    3r = 975 .......................(4) = (2) - (3)
    => r = 975/3
    => r = 325

    but r + g = 450
    => 325 + g = 450
    => g = 450 - 325
    => g = 125

    so 325 reserved tickets were sold and 125 general admission tickets were sold
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