There were 734 tickets purchased for a major league baseball

There were 734 tickets purchased for a major league baseball game. The lower box tickets cost $12.50 and the upper reserved tickets cost $8.00. The total amount of money spent was $7402.00. How many of each kind of ticket were purchased? How many lower box tickets were purchased? How many upper reserved tickets were purchased?

Solution

Given that

Total tickets purchased for major league baseball game = 734

Lower box tickets cost = $12.50

Upper reserved tickets cost = $8.00

Total amount of money spent on tickets = $7402.00

Let number of lower box tickets = x

   Number of upper reserved tickets = 734 - x

Hence,

   Total tickets cost = x($12.50) + (734 - x)($8.00)

           x($12.50) + (734 - x)($8.00) = $7402.00

                12.50x + 5872.00 - 8.00x = 7402.00

                           4.5x + 5872.00 = 7402.00

                                4.5x = 7402.00 - 5872.00

                                4.5x = 1530.00

                                    x = 1530.00/4.5

                                    x = 340

Hence,

    Number of lower box tickets x = 340

    Upper reserved tickets = 734 - x

                                         = 734 - 340

                                         = 394

Therefore,

          Number of lower box tickets   = 340

Number of upper reserved tickets    = 394