The museum tickets are priced at $14 and $9.  The number of $14-dollar tickets available is  2⁵₆ that of the number of $9-dollar tickets. 3 out of 5 of the $14-dollar tickets and all the $9-dollar tickets were sold. The ticket sales amounted to $10824. How much more would have been collected if all the tickets were sold?

	$14	$9
Comparing $14 and $9 tickets at first	17x5 = 85 u	6x5 = 30 u
Before	5x17 = 85 u
Change	- 3x17 = - 51 u	- 30 u
After	2x17 = 34 u	0 u

The number of 14 tickets at first is repeated.  Make the number of 14 tickets the same.  LCM of 5 and 17 is 85.

2⁵₆ = ¹⁷₆

Number of $14 tickets : $9 tickets = 17 : 6

	$14	$9	Total
Number	51 u	30 u
Value	$14	$9
Total value	714 u	270 u	$10824

Total amount collected from the sale of the sold tickets
= 714 u + 270 u
= 984 u

1 u = 10824 ÷ 984 = 11

Number of $14-tickets left unsold
= 34 u 
= 34 x 11
= 374

More amount to be collected if all the tickets were sold
= 374 x 14
= $5236

Answer(s): $5236