The ratio of the number of tarts in Container M to the number of tarts in Container N was 7 : 5. 20% of the tarts in Container M and 0.6 of those in Container N were matcha. After transferring the tarts between the 2 boxes, the number of peach tarts in both boxes are the same. Likewise, the number of matcha tarts in both boxes are the same. If a total of 169 tarts were moved, how many more tarts were there in Container M than Container N at first?

Container M		Container N
7 u		5 u
Matcha	Peach	Matcha	Peach
1.4 u	5.6 u	3 u	2 u
+ 0.8 u	- 1.8 u	- 0.8 u	+ 1.8 u
2.2 u	3.8 u	2.2 u	3.8 u

Number of matcha tarts in Container M
= 20% x 7 u
= ²⁰₁₀₀ x 7 u
= 1.4 u

Number of peach tarts in Container M
= 7 u - 1.4 u
= 5.6 u

Number of matcha tarts in Container N
= 0.6 x 5 u
= 3 u

Number of peach tarts in Container N
= 5 u - 3 u
= 2 u

Number of matcha tarts in each box in the end
= (1.4 u + 3 u) ÷ 2
= 4.4 u ÷ 2
= 2.2 u

Number of peach tarts in each box in the end
= (5.6 u + 2 u) ÷ 2
= 7.6 u ÷ 2
= 3.8 u

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

2.6 u = 169

1 u = 169 ÷ 2.6 = 65

Number of more tarts in Container M than Container N at first
= 7 u - 5 u
= 2 u
= 2 x 65
= 130

Answer(s): 130