The ratio of the number of cupcakes in Container P to the number of cupcakes in Container Q was 7 : 3. 20% of the cupcakes in Container P and 0.6 of those in Container Q were peach. After transferring the cupcakes between the 2 boxes, the number of strawberry cupcakes in both boxes are the same. Likewise, the number of peach cupcakes in both boxes are the same. If a total of 192 cupcakes were moved, how many more cupcakes were there in Container P than Container Q at first?

Container P		Container Q
7 u		3 u
Peach	Strawberry	Peach	Strawberry
1.4 u	5.6 u	1.8 u	1.2 u
+ 0.2 u	- 2.2 u	- 0.2 u	+ 2.2 u
1.6 u	3.4 u	1.6 u	3.4 u

Number of peach cupcakes in Container P
= 20% x 7 u
= ²⁰₁₀₀ x 7 u
= 1.4 u

Number of strawberry cupcakes in Container P
= 7 u - 1.4 u
= 5.6 u

Number of peach cupcakes in Container Q
= 0.6 x 3 u
= 1.8 u

Number of strawberry cupcakes in Container Q
= 3 u - 1.8 u
= 1.2 u

Number of peach cupcakes in each box in the end
= (1.4 u + 1.8 u) ÷ 2
= 3.2 u ÷ 2
= 1.6 u

Number of strawberry cupcakes in each box in the end
= (5.6 u + 1.2 u) ÷ 2
= 6.8 u ÷ 2
= 3.4 u

Number of cupcakes moved
= 0.2 u + 2.2 u
= 2.4 u

2.4 u = 192

1 u = 192 ÷ 2.4 = 80

Number of more cupcakes in Container P than Container Q at first
= 7 u - 3 u
= 4 u
= 4 x 80
= 320

Answer(s): 320