The ratio of the number of cupcakes in Container Q to the number of cupcakes in Container R was 7 : 3. 10% of the cupcakes in Container Q and 0.9 of those in Container R were vanilla. After transferring the cupcakes between the 2 boxes, the number of peach cupcakes in both boxes are the same. Likewise, the number of vanilla cupcakes in both boxes are the same. If a total of 200 cupcakes were moved, how many more cupcakes were there in Container Q than Container R at first?

Container Q		Container R
7 u		3 u
Vanilla	Peach	Vanilla	Peach
0.7 u	6.3 u	2.7 u	0.3 u
+ 1 u	- 3 u	- 1 u	+ 3 u
1.7 u	3.3 u	1.7 u	3.3 u

Number of vanilla cupcakes in Container Q
= 10% x 7 u
= ¹⁰₁₀₀ x 7 u
= 0.7 u

Number of peach cupcakes in Container Q
= 7 u - 0.7 u
= 6.3 u

Number of vanilla cupcakes in Container R
= 0.9 x 3 u
= 2.7 u

Number of peach cupcakes in Container R
= 3 u - 2.7 u
= 0.3 u

Number of vanilla cupcakes in each box in the end
= (0.7 u + 2.7 u) ÷ 2
= 3.4 u ÷ 2
= 1.7 u

Number of peach cupcakes in each box in the end
= (6.3 u + 0.3 u) ÷ 2
= 6.6 u ÷ 2
= 3.3 u

Number of cupcakes moved
= 1 u + 3 u
= 4 u

4 u = 200

1 u = 200 ÷ 4 = 50

Number of more cupcakes in Container Q than Container R at first
= 7 u - 3 u
= 4 u
= 4 x 50
= 200

Answer(s): 200