The ratio of the number of cupcakes in Container L to the number of cupcakes in Container M was 5 : 3. 30% of the cupcakes in Container L and 0.6 of those in Container M were chocolate. After transferring the cupcakes between the 2 containers, the number of cherry cupcakes in both containers are the same. Likewise, the number of chocolate cupcakes in both containers are the same. If a total of 286 cupcakes were moved, how many more cupcakes were there in Container L than Container M at first?

Container L		Container M
5 u		3 u
Chocolate	Cherry	Chocolate	Cherry
1.5 u	3.5 u	1.8 u	1.2 u
+ 0.15 u	- 1.15 u	- 0.15 u	+ 1.15 u
1.65 u	2.35 u	1.65 u	2.35 u

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

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

Number of chocolate cupcakes in Container M
= 0.6 x 3 u
= 1.8 u

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

Number of chocolate cupcakes in each container in the end
= (1.5 u + 1.8 u) ÷ 2
= 3.3 u ÷ 2
= 1.65 u

Number of cherry cupcakes in each container in the end
= (3.5 u + 1.2 u) ÷ 2
= 4.7 u ÷ 2
= 2.35 u

Number of cupcakes moved
= 0.15 u + 1.15 u
= 1.3 u

1.3 u = 286

1 u = 286 ÷ 1.3 = 220

Number of more cupcakes in Container L than Container M at first
= 5 u - 3 u
= 2 u
= 2 x 220
= 440

Answer(s): 440