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3 February, 14:40

On December 1, there were 52 more tickets to the Spring Fling unsold than sold. At that time, the sold tickets represented 30% of the total tickets available. Two weeks later, the percent of sold tickets had increased to 50% of the tickets that were available. How many tickets were sold during the 2-week period after December 1?

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  1. 3 February, 16:48
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    26 tickets were sold during that 2 week period.

    Let x be the number of tickets sold and y be the number of tickets unsold.

    Since the number of unsold is 52 more than the number sold, y=x+52.

    The number of tickets sold is 30% of the total number of tickets; this means

    x=0.3 (x+y)

    Using the distributive property,

    x=0.3*x+0.3*y

    x=0.3x+0.3y

    Substituting our value from the first equation in for y,

    x=0.3x+0.3 (x+52)

    Using the distributive property,

    x=0.3x+0.3*x+0.3*52

    x=0.3x+0.3x+15.6

    Combining like terms,

    x=0.6x+15.6

    Subtract 0.6x from both sides:

    x-0.6x = 0.6x+15.6-0.6x

    0.4x = 15.6

    Divide both sides by 0.4:

    0.4x/0.4 = 15.6/0.4

    x=39

    There were 39 tickets sold. This means there were 39+52=91 unsold tickets, and 39+91=130 tickets available.

    Two weeks later, 50% of tickets available were sold:

    0.5 (130) = 65 tickets sold

    This is a difference of 65-39 = 26 tickets.
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