A convenience store sold jam, club and ham sandwiches. The ratio of the number of jam sandwiches made to the total number of sandwiches made was 5 : 7. The ratio of the number of club sandwiches made to the total number of sandwiches made was 1 : 9. After the store sold some jam sandwiches and made another 24 club sandwiches, there was an equal number of jam, club and ham sandwiches left. Find the number of jam sandwiches sold.

	Jam	Club	Ham	Total
Comparing jam to total	5x9			7x9
Comparing  club to total		1x7		9x7
	45 u	7 u	11 u	63 u

	Jam	Club	Ham	Total
Before	45 u	7 u	11 u	63 u
Change	- 34 u	+ 24	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 9 and 7 is 63.

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

Number of ham sandwiches 
= 63 u - 45 u - 7 u
= 11 u

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

Number of club sandwiches = 7 u + 24

7 u + 24 = 11 u
11 u - 7 u = 24
4 u = 24

1 u = 24 ÷ 4 = 6

Number of jam sandwiches sold
= 45 u - 11 u
= 34 u
= 34 x 6
= 204

Answer(s): 204