The ratio of the number of tarts in Container R to the number of tarts in Container S was 5 : 3. 30% of the tarts in Container R and 0.6 of those in Container S were vanilla. After transferring the tarts between the 2 containers, the number of chocolate tarts in both containers are the same. Likewise, the number of vanilla tarts in both containers are the same. If a total of 260 tarts were moved, how many more tarts were there in Container R than Container S at first?

Container R		Container S
5 u		3 u
Vanilla	Chocolate	Vanilla	Chocolate
1.5 u	3.5 u	1.8 u	1.2 u
+ 0.15 u	- 1.15 u	- 0.15 u	+ 1.15 u
1.65 u	2.35 u	1.65 u	2.35 u

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

Number of chocolate tarts in Container R
= 5 u - 1.5 u
= 3.5 u

Number of vanilla tarts in Container S
= 0.6 x 3 u
= 1.8 u

Number of chocolate tarts in Container S
= 3 u - 1.8 u
= 1.2 u

Number of vanilla tarts in each container in the end
= (1.5 u + 1.8 u) ÷ 2
= 3.3 u ÷ 2
= 1.65 u

Number of chocolate tarts in each container in the end
= (3.5 u + 1.2 u) ÷ 2
= 4.7 u ÷ 2
= 2.35 u

Number of tarts moved
= 0.15 u + 1.15 u
= 1.3 u

1.3 u = 260

1 u = 260 ÷ 1.3 = 200

Number of more tarts in Container R than Container S at first
= 5 u - 3 u
= 2 u
= 2 x 200
= 400

Answer(s): 400