The ratio of the number of biscuits in Container Y to the number of biscuits in Container Z was 5 : 3. 30% of the biscuits in Container Y and 0.6 of those in Container Z were matcha. After transferring the biscuits between the 2 boxes, the number of mocha biscuits in both boxes are the same. Likewise, the number of matcha biscuits in both boxes are the same. If a total of 260 biscuits were moved, how many more biscuits were there in Container Y than Container Z at first?

Container Y		Container Z
5 u		3 u
Matcha	Mocha	Matcha	Mocha
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 matcha biscuits in Container Y
= 30% x 5 u
= ³⁰₁₀₀ x 5 u
= 1.5 u

Number of mocha biscuits in Container Y
= 5 u - 1.5 u
= 3.5 u

Number of matcha biscuits in Container Z
= 0.6 x 3 u
= 1.8 u

Number of mocha biscuits in Container Z
= 3 u - 1.8 u
= 1.2 u

Number of matcha biscuits in each box in the end
= (1.5 u + 1.8 u) ÷ 2
= 3.3 u ÷ 2
= 1.65 u

Number of mocha biscuits in each box in the end
= (3.5 u + 1.2 u) ÷ 2
= 4.7 u ÷ 2
= 2.35 u

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

1.3 u = 260

1 u = 260 ÷ 1.3 = 200

Number of more biscuits in Container Y than Container Z at first
= 5 u - 3 u
= 2 u
= 2 x 200
= 400

Answer(s): 400