The ratio of the number of tarts in Container C to the number of tarts in Container D was 5 : 3. 30% of the tarts in Container C and 0.9 of those in Container D were vanilla. After transferring the tarts between the 2 boxes, the number of cherry tarts in both boxes are the same. Likewise, the number of vanilla tarts in both boxes are the same. If a total of 198 tarts were moved, how many more tarts were there in Container C than Container D at first?

Container C		Container D
5 u		3 u
Vanilla	Cherry	Vanilla	Cherry
1.5 u	3.5 u	2.7 u	0.3 u
+ 0.6 u	- 1.6 u	- 0.6 u	+ 1.6 u
2.1 u	1.9 u	2.1 u	1.9 u

Number of vanilla tarts in Container C
= 30% x 5 u
= ³⁰₁₀₀ x 5 u
= 1.5 u

Number of cherry tarts in Container C
= 5 u - 1.5 u
= 3.5 u

Number of vanilla tarts in Container D
= 0.9 x 3 u
= 2.7 u

Number of cherry tarts in Container D
= 3 u - 2.7 u
= 0.3 u

Number of vanilla tarts in each box in the end
= (1.5 u + 2.7 u) ÷ 2
= 4.2 u ÷ 2
= 2.1 u

Number of cherry tarts in each box in the end
= (3.5 u + 0.3 u) ÷ 2
= 3.8 u ÷ 2
= 1.9 u

Number of tarts moved
= 0.6 u + 1.6 u
= 2.2 u

2.2 u = 198

1 u = 198 ÷ 2.2 = 90

Number of more tarts in Container C than Container D at first
= 5 u - 3 u
= 2 u
= 2 x 90
= 180

Answer(s): 180