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.