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

If there are x reserved seats, receipts were

1.50x + .05*25x = 2.75x
Now, we want y reserved $1 seats to fetch the same money:

1.00y + .05(26x-y) = 2.75x

y + 1.3x - .05y = 2.75x
.95y = 1.45x
y/x = 1.45/.95 = .29/.19 = 29/19

So, now we want y/26x = 29/494

The ratio of reserved to unreserved is thus 29/465

Check:
If there are 494 seats, there were originally

19 @ 1.50 = 28.50
475 @ .05 = 23.75
total: 52.25

Now, there are
29 @ 1.00 = 29.00
465 @ .05 = 23.25
total: 52.25

Naturally, any multiples of 494 will also work.