The ratio of the number of tarts in Container C to the number of tarts in Container D was 9 : 5. 10% of the tarts in Container C and 0.8 of those in Container D were chocolate. After transferring the tarts between the 2 boxes, the number of peach tarts in both boxes are the same. Likewise, the number of chocolate tarts in both boxes are the same. If a total of 204 tarts were moved, how many more tarts were there in Container C than Container D at first?

Container C		Container D
9 u		5 u
Chocolate	Peach	Chocolate	Peach
0.9 u	8.1 u	4 u	1 u
+ 1.55 u	- 3.55 u	- 1.55 u	+ 3.55 u
2.45 u	4.55 u	2.45 u	4.55 u

Number of chocolate tarts in Container C
= 10% x 9 u
= ¹⁰₁₀₀ x 9 u
= 0.9 u

Number of peach tarts in Container C
= 9 u - 0.9 u
= 8.1 u

Number of chocolate tarts in Container D
= 0.8 x 5 u
= 4 u

Number of peach tarts in Container D
= 5 u - 4 u
= 1 u

Number of chocolate tarts in each box in the end
= (0.9 u + 4 u) ÷ 2
= 4.9 u ÷ 2
= 2.45 u

Number of peach tarts in each box in the end
= (8.1 u + 1 u) ÷ 2
= 9.1 u ÷ 2
= 4.55 u

Number of tarts moved
= 1.55 u + 3.55 u
= 5.1 u

5.1 u = 204

1 u = 204 ÷ 5.1 = 40

Number of more tarts in Container C than Container D at first
= 9 u - 5 u
= 4 u
= 4 x 40
= 160

Answer(s): 160