The ratio of the number of cupcakes in Container G to the number of cupcakes in Container H was 5 : 3. 10% of the cupcakes in Container G and 0.6 of those in Container H were butter cream. After transferring the cupcakes between the 2 boxes, the number of cherry cupcakes in both boxes are the same. Likewise, the number of butter cream cupcakes in both boxes are the same. If a total of 184 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
Butter Cream	Cherry	Butter Cream	Cherry
0.5 u	4.5 u	1.8 u	1.2 u
+ 0.65 u	- 1.65 u	- 0.65 u	+ 1.65 u
1.15 u	2.85 u	1.15 u	2.85 u

Number of butter cream cupcakes in Container G
= 10% x 5 u
= ¹⁰₁₀₀ x 5 u
= 0.5 u

Number of cherry cupcakes in Container G
= 5 u - 0.5 u
= 4.5 u

Number of butter cream cupcakes in Container H
= 0.6 x 3 u
= 1.8 u

Number of cherry cupcakes in Container H
= 3 u - 1.8 u
= 1.2 u

Number of butter cream cupcakes in each box in the end
= (0.5 u + 1.8 u) ÷ 2
= 2.3 u ÷ 2
= 1.15 u

Number of cherry cupcakes in each box in the end
= (4.5 u + 1.2 u) ÷ 2
= 5.7 u ÷ 2
= 2.85 u

Number of cupcakes moved
= 0.65 u + 1.65 u
= 2.3 u

2.3 u = 184

1 u = 184 ÷ 2.3 = 80

Number of more cupcakes in Container G than Container H at first
= 5 u - 3 u
= 2 u
= 2 x 80
= 160

Answer(s): 160