The ratio of the number of biscuits in Container M to the number of biscuits in Container N was 5 : 3. 10% of the biscuits in Container M and 0.7 of those in Container N were butter cream. After transferring the biscuits between the 2 boxes, the number of vanilla biscuits in both boxes are the same. Likewise, the number of butter cream biscuits in both boxes are the same. If a total of 286 biscuits were moved, how many more biscuits were there in Container M than Container N at first?

Container M		Container N
5 u		3 u
Butter Cream	Vanilla	Butter Cream	Vanilla
0.5 u	4.5 u	2.1 u	0.9 u
+ 0.8 u	- 1.8 u	- 0.8 u	+ 1.8 u
1.3 u	2.7 u	1.3 u	2.7 u

Number of butter cream biscuits in Container M
= 10% x 5 u
= ¹⁰₁₀₀ x 5 u
= 0.5 u

Number of vanilla biscuits in Container M
= 5 u - 0.5 u
= 4.5 u

Number of butter cream biscuits in Container N
= 0.7 x 3 u
= 2.1 u

Number of vanilla biscuits in Container N
= 3 u - 2.1 u
= 0.9 u

Number of butter cream biscuits in each box in the end
= (0.5 u + 2.1 u) ÷ 2
= 2.6 u ÷ 2
= 1.3 u

Number of vanilla biscuits in each box in the end
= (4.5 u + 0.9 u) ÷ 2
= 5.4 u ÷ 2
= 2.7 u

Number of biscuits moved
= 0.8 u + 1.8 u
= 2.6 u

2.6 u = 286

1 u = 286 ÷ 2.6 = 110

Number of more biscuits in Container M than Container N at first
= 5 u - 3 u
= 2 u
= 2 x 110
= 220

Answer(s): 220