What is the area of square QROS if the area of MNOP is 64? The figure below shows a square region divided into four rectangular regions, three of which have areas 5x, 5x, and, respectively.

One way to solve this problem is to set up an equation using one variable. Let n represent the number of 3 dollars tickets sold; then 50 minus n represents the number of 5 dollars tickets sold.
(3 times n) + (5 times (50 minus n)) = 230
(3 times n) +250 minus (5 times n) = 230
20 = 2 times n
10 = n
There were 10 3 dollar tickets sold.
Simultaneous equations can also be set up to solve the problem. Let n represent the number of 3 dollar tickets sold and p represent the number of 5 dollar tickets sold.
n + p = 50
(3 times n) + (5 times p) = 230
Another way to solve this problem is to realize that each of the tickets costs at least 3 dollars. At 3 dollars each, a total of 150 dollars would be collected from selling all 50 of the tickets. Since the remaining 80 dollars was the extra 2 dollars collected from each of the 5 dollar tickets, 40 of the 5 dollar tickets were sold. This implies that 10 of the 3 dollar tickets were sold.