The ratio of the number of cupcakes in Container K to the number of cupcakes in Container L was 5 : 3. 30% of the cupcakes in Container K and 0.7 of those in Container L were butter cream. After transferring the cupcakes between the 2 containers, the number of mocha cupcakes in both containers are the same. Likewise, the number of butter cream cupcakes in both containers are the same. If a total of 160 cupcakes were moved, how many more cupcakes were there in Container K than Container L at first?

Container K		Container L
5 u		3 u
Butter Cream	Mocha	Butter Cream	Mocha
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 butter cream cupcakes in Container K
= 30% x 5 u
= ³⁰₁₀₀ x 5 u
= 1.5 u

Number of mocha cupcakes in Container K
= 5 u - 1.5 u
= 3.5 u

Number of butter cream cupcakes in Container L
= 0.7 x 3 u
= 2.1 u

Number of mocha cupcakes in Container L
= 3 u - 2.1 u
= 0.9 u

Number of butter cream cupcakes in each container in the end
= (1.5 u + 2.1 u) ÷ 2
= 3.6 u ÷ 2
= 1.8 u

Number of mocha cupcakes in each container 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 = 160

1 u = 160 ÷ 1.6 = 100

Number of more cupcakes in Container K than Container L at first
= 5 u - 3 u
= 2 u
= 2 x 100
= 200

Answer(s): 200