A major league baseball stadium sells three types of tickets. Reserved tickets are sold for $20 each, field-level tickets are sold for $50 each, and box seat tickets are sold $100 each. You purchase 10 total tickets for $370. You have twice as many reserved tickets as field-level tickets. How many tickets of each do you have?

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23-08-2022
Mathematics

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A major league baseball stadium sells three types of tickets. Reserved tickets are sold for $20 each, field-level tickets are sold for $50 each, and box seat tickets are sold $100 each. You purchase 10 total tickets for $370. You have twice as many reserved tickets as field-level tickets. How many tickets of each do you have?

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okpalawalter8 okpalawalter8 · Answer 1 · 2022-08-24T20:45:28+02:00

There were six reserved tickets, three tickets for the field level, and one ticket for the box seat.

How many tickets for each do you have?

Let's say that x stands for the number of tickets that have been reserved, y stands for the number of tickets at the field level, and z stands for the number of tickets in the box seats.

Taking into consideration that a total of 10 tickets cost $370, the following equation may be used to express this data:

20x + 50y + 100z = 370........ (1)

x + y + z = 10 (2)

In addition, there were two times as many tickets for reserved seating as there were for field-level seating. The following equation may be used to express this:

x = 2y

x - 2y = 0...... (3)

The result of concurrently solving equations 1, 2, and 3 is that

x equals 6, y equals 3, and z equals 1

There were six reserved tickets, three tickets for the field level, and one ticket for the box seat.