Question

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?

Answer 1

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.