The ratio of the number of cupcakes in Container H to the number of cupcakes in Container J was 7 : 3. 10% of the cupcakes in Container H and 0.9 of those in Container J were mango. After transferring the cupcakes between the 2 containers, the number of chocolate cupcakes in both containers are the same. Likewise, the number of mango cupcakes in both containers are the same. If a total of 264 cupcakes were moved, how many more cupcakes were there in Container H than Container J at first?

Container H		Container J
7 u		3 u
Mango	Chocolate	Mango	Chocolate
0.7 u	6.3 u	2.7 u	0.3 u
+ 1 u	- 3 u	- 1 u	+ 3 u
1.7 u	3.3 u	1.7 u	3.3 u

Number of mango cupcakes in Container H
= 10% x 7 u
= ¹⁰₁₀₀ x 7 u
= 0.7 u

Number of chocolate cupcakes in Container H
= 7 u - 0.7 u
= 6.3 u

Number of mango cupcakes in Container J
= 0.9 x 3 u
= 2.7 u

Number of chocolate cupcakes in Container J
= 3 u - 2.7 u
= 0.3 u

Number of mango cupcakes in each container in the end
= (0.7 u + 2.7 u) ÷ 2
= 3.4 u ÷ 2
= 1.7 u

Number of chocolate cupcakes in each container in the end
= (6.3 u + 0.3 u) ÷ 2
= 6.6 u ÷ 2
= 3.3 u

Number of cupcakes moved
= 1 u + 3 u
= 4 u

4 u = 264

1 u = 264 ÷ 4 = 66

Number of more cupcakes in Container H than Container J at first
= 7 u - 3 u
= 4 u
= 4 x 66
= 264

Answer(s): 264