The ratio of the number of cupcakes in Container G to the number of cupcakes in Container H was 5 : 3. 30% of the cupcakes in Container G and 0.7 of those in Container H were chocolate. After transferring the cupcakes between the 2 boxes, the number of cherry cupcakes in both boxes are the same. Likewise, the number of chocolate cupcakes in both boxes are the same. If a total of 272 cupcakes were moved, how many more cupcakes were there in Container G than Container H at first?

Container G		Container H
5 u		3 u
Chocolate	Cherry	Chocolate	Cherry
1.5 u	3.5 u	2.1 u	0.9 u
+ 0.3 u	- 1.3 u	- 0.3 u	+ 1.3 u
1.8 u	2.2 u	1.8 u	2.2 u

Number of chocolate cupcakes in Container G
= 30% x 5 u
= ³⁰₁₀₀ x 5 u
= 1.5 u

Number of cherry cupcakes in Container G
= 5 u - 1.5 u
= 3.5 u

Number of chocolate cupcakes in Container H
= 0.7 x 3 u
= 2.1 u

Number of cherry cupcakes in Container H
= 3 u - 2.1 u
= 0.9 u

Number of chocolate cupcakes in each box in the end
= (1.5 u + 2.1 u) ÷ 2
= 3.6 u ÷ 2
= 1.8 u

Number of cherry cupcakes in each box in the end
= (3.5 u + 0.9 u) ÷ 2
= 4.4 u ÷ 2
= 2.2 u

Number of cupcakes moved
= 0.3 u + 1.3 u
= 1.6 u

1.6 u = 272

1 u = 272 ÷ 1.6 = 170

Number of more cupcakes in Container G than Container H at first
= 5 u - 3 u
= 2 u
= 2 x 170
= 340

Answer(s): 340