For the first of two basketball games the price of each reserved seat was $1.50,the price of each unreserved seat was 5 cents, and the number of reserved seats sold was 1/25 of the number of unreserved seats sold.If, at a second game, the price of the reserved seats is to be reduced to $1.00,what proportion should be reserved to give the same receipts, provided the same number of seats are sold?

Question

For the first of two basketball games the price of each reserved seat was $1.50,the price of each unreserved seat was 5 cents, and the number of reserved seats sold was 1/25 of the number of unreserved seats sold.If, at a second game, the price of the reserved seats is to be reduced to $1.00,what proportion should be reserved to give the same receipts, provided the same number of seats are sold?

Answer 1

To find the proportion of reserved seats that should be sold at the second game to give the same receipts, we need to determine the ratio between the prices of the reserved and unreserved seats at each game.

Let's first analyze the information provided for the first game:

- Price of reserved seats: $1.50
- Price of unreserved seats: $0.05
- Number of reserved seats sold: (1/25) * number of unreserved seats sold.

To calculate the ratio of reserved to unreserved seat prices, we divide the price of reserved seats by the price of unreserved seats:

Ratio at the first game = ($1.50) / ($0.05) = 30

This means the price of reserved seats is 30 times the price of unreserved seats.

Now, for the second game, the price of reserved seats is reduced to $1.00. We need to determine the proportion of reserved seats that should be sold to maintain the same receipts.

Let's assume the number of seats sold at both games remains the same.

To find the ratio of reserved to unreserved seat prices for the second game, we divide the new price of reserved seats by the price of unreserved seats:

Ratio at the second game = ($1.00) / ($0.05) = 20

To maintain the same receipts as the first game, the proportion of reserved seats sold at the second game should be the same as the ratio between the reserved and unreserved seat prices at the second game compared to the first game.

Proportion of reserved seats sold at the second game = Ratio at the second game / Ratio at the first game

Proportion of reserved seats sold at the second game = 20 / 30 = 2/3

Therefore, 2/3 or approximately 0.67 of the seats should be reserved to give the same receipts at the second game, provided the same number of seats are sold.