A convenience store sold chicken, jam and egg mayo sandwiches. The ratio of the number of chicken sandwiches made to the total number of sandwiches made was 4 : 7. The ratio of the number of jam sandwiches made to the total number of sandwiches made was 1 : 9. After the store sold some chicken sandwiches and made another 24 jam sandwiches, there was an equal number of chicken, jam and egg mayo sandwiches left. Find the number of chicken sandwiches sold.

	Chicken	Jam	Egg Mayo	Total
Comparing chicken to total	4x9			7x9
Comparing  jam to total		1x7		9x7
	36 u	7 u	20 u	63 u

	Chicken	Jam	Egg Mayo	Total
Before	36 u	7 u	20 u	63 u
Change	- 16 u	+ 24	No change
After	1x20 = 20 u	1x20 = 20 u	1x20 = 20 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 egg mayo sandwiches remains the same at first and in the end. Make the number of egg mayo sandwiches the  same. LCM of 1 and 20 is 20.

Number of egg mayo sandwiches 
= 63 u - 36 u - 7 u
= 20 u

Number of chicken, jam and egg mayo sandwiches is the same in the end. 

Number of jam sandwiches = 7 u + 24

7 u + 24 = 20 u
20 u - 7 u = 24
13 u = 24

1 u = 24 ÷ 13 = 4

Number of chicken sandwiches sold
= 36 u - 20 u
= 16 u
= 16 x 4
= 64

Answer(s): 64