There were some pink coins and grey coins. The coins were packed into 2 bags. At first, Box Y contained 170 coins and 30% of them were grey coins. Box Z contained 160 coins and 75% of them were grey coins. How many pink coins and grey coins in total must be moved from Box Y to Box Z such that 20% of the coins in Box Y are pink and 50% of the coins in Box Z are grey?

	Box Y		Box Z
Total	170		160
	Grey coins	Pink coins	Grey coins	Pink coins
Before	51	119	120	40
Change	- ?	- ?	+ ?	+ ?
After	4 u	1 u	1 p	1 p

Number of grey coins in Box Y at first
= 30% x 170
= ³⁰₁₀₀ x 170
= 51

Number of pink coins in Box Y at first
= 170 - 51
= 119

Number of grey coins in Box Z at first
= 75% x 160
= ⁷⁵₁₀₀ x 160
= 120

Number of pink coins in Box Z at first
= 160 - 120
= 40

Box Y in the end
20% = ²⁰₁₀₀ =¹₅
Grey coins : Pink coins = 4 : 1

Box Z in the end
50% = ⁵⁰₁₀₀ =¹₂
Grey coins : Pink coins = 1 : 1

Total number of grey coins = 4 u + 1 p

4 u + 1 p = 51 + 120
4 u + 1 p = 171 

1 p = 171 - 4 u --- (1)

Total number of pink coins = 1 u + 1 p
1 u + 1 p = 119 + 40
1 u + 1 p = 159

1 p = 159 - 1 u --- (2)

(2) = (1)
159 - 1 u = 171 - 4 u
4 u - 1 u = 171 - 159
3 u = 12

1 u = 12 ÷ 3 = 4

Total number of pink coins and grey coins that must be moved from Box Y to Box Z
= 170 - 5 u
= 170 - 5 x 4
= 170 - 20
= 150

Answer(s): 150