A convenience store sold bacon, ham and jam sandwiches. The ratio of the number of bacon sandwiches made to the total number of sandwiches made was 3 : 5. The ratio of the number of ham sandwiches made to the total number of sandwiches made was 1 : 8. After the store sold some bacon sandwiches and made another 21 ham sandwiches, there was an equal number of bacon, ham and jam sandwiches left. Find the number of bacon sandwiches sold.

	Bacon	Ham	Jam	Total
Comparing bacon to total	3x8			5x8
Comparing  ham to total		1x5		8x5
	24 u	5 u	11 u	40 u

	Bacon	Ham	Jam	Total
Before	24 u	5 u	11 u	40 u
Change	- 13 u	+ 21	No change
After	1x11 = 11 u	1x11 = 11 u	1x11 = 11 u

The total number of sandwiches is the same at first. Make the total number of sandwiches the same.  LCM of 8 and 5 is 40.

Number of jam sandwiches remains the same at first and in the end. Make the number of jam sandwiches the  same. LCM of 1 and 11 is 11.

Number of jam sandwiches 
= 40 u - 24 u - 5 u
= 11 u

Number of bacon, ham and jam sandwiches is the same in the end. 

Number of ham sandwiches = 5 u + 21

5 u + 21 = 11 u
11 u - 5 u = 21
6 u = 21

1 u = 21 ÷ 6 = 6

Number of bacon sandwiches sold
= 24 u - 11 u
= 13 u
= 13 x 6
= 78

Answer(s): 78