There were some purple coins and yellow coins. The coins were packed into 2 bags. At first, Bag R contained 180 coins and 30% of them were yellow coins. Bag S contained 140 coins and 80% of them were yellow coins. How many purple coins and yellow coins in total must be moved from Bag R to Bag S such that 20% of the coins in Bag R are purple and 50% of the coins in Bag S are yellow?

	Bag R		Bag S
Total	180		140
	Yellow coins	Purple coins	Yellow coins	Purple coins
Before	54	126	112	28
Change	- ?	- ?	+ ?	+ ?
After	4 u	1 u	1 p	1 p

Number of yellow coins in Bag R at first
= 30% x 180
= ³⁰₁₀₀ x 180
= 54

Number of purple coins in Bag R at first
= 180 - 54
= 126

Number of yellow coins in Bag S at first
= 80% x 140
= ⁸⁰₁₀₀ x 140
= 112

Number of purple coins in Bag S at first
= 140 - 112
= 28

Bag R in the end
20% = ²⁰₁₀₀ =¹₅
Yellow coins : Purple coins = 4 : 1

Bag S in the end
50% = ⁵⁰₁₀₀ =¹₂
Yellow coins : Purple coins = 1 : 1

Total number of yellow coins = 4 u + 1 p

4 u + 1 p = 54 + 112
4 u + 1 p = 166 

1 p = 166 - 4 u --- (1)

Total number of purple coins = 1 u + 1 p
1 u + 1 p = 126 + 28
1 u + 1 p = 154

1 p = 154 - 1 u --- (2)

(2) = (1)
154 - 1 u = 166 - 4 u
4 u - 1 u = 166 - 154
3 u = 12

1 u = 12 ÷ 3 = 4

Total number of purple coins and yellow coins that must be moved from Bag R to Bag S
= 180 - 5 u
= 180 - 5 x 4
= 180 - 20
= 160

Answer(s): 160