There were some purple marbles and gold marbles. The marbles were packed into 2 bags. At first, Packet A contained 270 marbles and 30% of them were gold marbles. Packet B contained 740 marbles and 60% of them were gold marbles. How many purple marbles and gold marbles in total must be moved from Packet A to Packet B such that 30% of the marbles in Packet A are purple and 50% of the marbles in Packet B are gold?

	Packet A		Packet B
Total	270		740
	Gold marbles	Purple marbles	Gold marbles	Purple marbles
Before	81	189	444	296
Change	- ?	- ?	+ ?	+ ?
After	7 u	3 u	1 p	1 p

Number of gold marbles in Packet A at first
= 30% x 270
= ³⁰₁₀₀ x 270
= 81

Number of purple marbles in Packet A at first
= 270 - 81
= 189

Number of gold marbles in Packet B at first
= 60% x 740
= ⁶⁰₁₀₀ x 740
= 444

Number of purple marbles in Packet B at first
= 740 - 444
= 296

Packet A in the end
30% = ³⁰₁₀₀ =³₁₀
Gold marbles : Purple marbles = 7 : 3

Packet B in the end
50% = ⁵⁰₁₀₀ =¹₂
Gold marbles : Purple marbles = 1 : 1

Total number of gold marbles = 7 u + 1 p

7 u + 1 p = 81 + 444
7 u + 1 p = 525 

1 p = 525 - 7 u --- (1)

Total number of purple marbles = 3 u + 1 p
3 u + 1 p = 189 + 296
3 u + 1 p = 485

1 p = 485 - 3 u --- (2)

(2) = (1)
485 - 3 u = 525 - 7 u
7 u - 3 u = 525 - 485
4 u = 40

1 u = 40 ÷ 4 = 10

Total number of purple marbles and gold marbles that must be moved from Packet A to Packet B
= 270 - 10 u
= 270 - 10 x 10
= 270 - 100
= 170

Answer(s): 170