The ratio of the number of cupcakes in Container N to the number of cupcakes in Container P was 7 : 5. 20% of the cupcakes in Container N and 0.6 of those in Container P were vanilla. After transferring the cupcakes between the 2 boxes, the number of butter cream cupcakes in both boxes are the same. Likewise, the number of vanilla cupcakes in both boxes are the same. If a total of 195 cupcakes were moved, how many more cupcakes were there in Container N than Container P at first?

Container N		Container P
7 u		5 u
Vanilla	Butter Cream	Vanilla	Butter Cream
1.4 u	5.6 u	3 u	2 u
+ 0.8 u	- 1.8 u	- 0.8 u	+ 1.8 u
2.2 u	3.8 u	2.2 u	3.8 u

Number of vanilla cupcakes in Container N
= 20% x 7 u
= ²⁰₁₀₀ x 7 u
= 1.4 u

Number of butter cream cupcakes in Container N
= 7 u - 1.4 u
= 5.6 u

Number of vanilla cupcakes in Container P
= 0.6 x 5 u
= 3 u

Number of butter cream cupcakes in Container P
= 5 u - 3 u
= 2 u

Number of vanilla cupcakes in each box in the end
= (1.4 u + 3 u) ÷ 2
= 4.4 u ÷ 2
= 2.2 u

Number of butter cream cupcakes in each box in the end
= (5.6 u + 2 u) ÷ 2
= 7.6 u ÷ 2
= 3.8 u

Number of cupcakes moved
= 0.8 u + 1.8 u
= 2.6 u

2.6 u = 195

1 u = 195 ÷ 2.6 = 75

Number of more cupcakes in Container N than Container P at first
= 7 u - 5 u
= 2 u
= 2 x 75
= 150

Answer(s): 150