The ratio of the number of cupcakes in Container J to the number of cupcakes in Container K was 5 : 3. 20% of the cupcakes in Container J and 0.8 of those in Container K were chocolate. After transferring the cupcakes between the 2 containers, the number of mocha cupcakes in both containers are the same. Likewise, the number of chocolate cupcakes in both containers are the same. If a total of 216 cupcakes were moved, how many more cupcakes were there in Container J than Container K at first?

Container J		Container K
5 u		3 u
Chocolate	Mocha	Chocolate	Mocha
1 u	4 u	2.4 u	0.6 u
+ 0.7 u	- 1.7 u	- 0.7 u	+ 1.7 u
1.7 u	2.3 u	1.7 u	2.3 u

Number of chocolate cupcakes in Container J
= 20% x 5 u
= ²⁰₁₀₀ x 5 u
= 1 u

Number of mocha cupcakes in Container J
= 5 u - 1 u
= 4 u

Number of chocolate cupcakes in Container K
= 0.8 x 3 u
= 2.4 u

Number of mocha cupcakes in Container K
= 3 u - 2.4 u
= 0.6 u

Number of chocolate cupcakes in each container in the end
= (1 u + 2.4 u) ÷ 2
= 3.4 u ÷ 2
= 1.7 u

Number of mocha cupcakes in each container in the end
= (4 u + 0.6 u) ÷ 2
= 4.6 u ÷ 2
= 2.3 u

Number of cupcakes moved
= 0.7 u + 1.7 u
= 2.4 u

2.4 u = 216

1 u = 216 ÷ 2.4 = 90

Number of more cupcakes in Container J than Container K at first
= 5 u - 3 u
= 2 u
= 2 x 90
= 180

Answer(s): 180