There were some pink coins and black coins. The coins were packed into 2 bags. At first, Box T contained 110 coins and 40% of them were black coins. Box U contained 50 coins and 80% of them were black coins. How many pink coins and black coins in total must be moved from Box T to Box U such that 25% of the coins in Box T are pink and 50% of the coins in Box U are black?

	Box T		Box U
Total	110		50
	Black coins	Pink coins	Black coins	Pink coins
Before	44	66	40	10
Change	- ?	- ?	+ ?	+ ?
After	3 u	1 u	1 p	1 p

Number of black coins in Box T at first
= 40% x 110
= ⁴⁰₁₀₀ x 110
= 44

Number of pink coins in Box T at first
= 110 - 44
= 66

Number of black coins in Box U at first
= 80% x 50
= ⁸⁰₁₀₀ x 50
= 40

Number of pink coins in Box U at first
= 50 - 40
= 10

Box T in the end
25% = ²⁵₁₀₀ =¹₄
Black coins : Pink coins = 3 : 1

Box U in the end
50% = ⁵⁰₁₀₀ =¹₂
Black coins : Pink coins = 1 : 1

Total number of black coins = 3 u + 1 p

3 u + 1 p = 44 + 40
3 u + 1 p = 84 

1 p = 84 - 3 u --- (1)

Total number of pink coins = 1 u + 1 p
1 u + 1 p = 66 + 10
1 u + 1 p = 76

1 p = 76 - 1 u --- (2)

(2) = (1)
76 - 1 u = 84 - 3 u
3 u - 1 u = 84 - 76
2 u = 8

1 u = 8 ÷ 2 = 4

Total number of pink coins and black coins that must be moved from Box T to Box U
= 110 - 4 u
= 110 - 4 x 4
= 110 - 16
= 94

Answer(s): 94