The ratio of the number of cupcakes in Container Y to the number of cupcakes in Container Z was 7 : 5. 10% of the cupcakes in Container Y and 0.8 of those in Container Z were cherry. After transferring the cupcakes between the 2 boxes, the number of mango cupcakes in both boxes are the same. Likewise, the number of cherry cupcakes in both boxes are the same. If a total of 258 cupcakes were moved, how many more cupcakes were there in Container Y than Container Z at first?

Container Y		Container Z
7 u		5 u
Cherry	Mango	Cherry	Mango
0.7 u	6.3 u	4 u	1 u
+ 1.65 u	- 2.65 u	- 1.65 u	+ 2.65 u
2.35 u	3.65 u	2.35 u	3.65 u

Number of cherry cupcakes in Container Y
= 10% x 7 u
= ¹⁰₁₀₀ x 7 u
= 0.7 u

Number of mango cupcakes in Container Y
= 7 u - 0.7 u
= 6.3 u

Number of cherry cupcakes in Container Z
= 0.8 x 5 u
= 4 u

Number of mango cupcakes in Container Z
= 5 u - 4 u
= 1 u

Number of cherry cupcakes in each box in the end
= (0.7 u + 4 u) ÷ 2
= 4.7 u ÷ 2
= 2.35 u

Number of mango cupcakes in each box in the end
= (6.3 u + 1 u) ÷ 2
= 7.3 u ÷ 2
= 3.65 u

Number of cupcakes moved
= 1.65 u + 2.65 u
= 4.3 u

4.3 u = 258

1 u = 258 ÷ 4.3 = 60

Number of more cupcakes in Container Y than Container Z at first
= 7 u - 5 u
= 2 u
= 2 x 60
= 120

Answer(s): 120