There were some gold marbles and purple marbles. The marbles were packed into 2 bags. At first, Box K contained 230 marbles and 30% of them were purple marbles. Box L contained 535 marbles and 60% of them were purple marbles. How many gold marbles and purple marbles in total must be moved from Box K to Box L such that 20% of the marbles in Box K are gold and 50% of the marbles in Box L are purple?

	Box K		Box L
Total	230		535
	Purple marbles	Gold marbles	Purple marbles	Gold marbles
Before	69	161	321	214
Change	- ?	- ?	+ ?	+ ?
After	4 u	1 u	1 p	1 p

Number of purple marbles in Box K at first
= 30% x 230
= ³⁰₁₀₀ x 230
= 69

Number of gold marbles in Box K at first
= 230 - 69
= 161

Number of purple marbles in Box L at first
= 60% x 535
= ⁶⁰₁₀₀ x 535
= 321

Number of gold marbles in Box L at first
= 535 - 321
= 214

Box K in the end
20% = ²⁰₁₀₀ =¹₅
Purple marbles : Gold marbles = 4 : 1

Box L in the end
50% = ⁵⁰₁₀₀ =¹₂
Purple marbles : Gold marbles = 1 : 1

Total number of purple marbles = 4 u + 1 p

4 u + 1 p = 69 + 321
4 u + 1 p = 390 

1 p = 390 - 4 u --- (1)

Total number of gold marbles = 1 u + 1 p
1 u + 1 p = 161 + 214
1 u + 1 p = 375

1 p = 375 - 1 u --- (2)

(2) = (1)
375 - 1 u = 390 - 4 u
4 u - 1 u = 390 - 375
3 u = 15

1 u = 15 ÷ 3 = 5

Total number of gold marbles and purple marbles that must be moved from Box K to Box L
= 230 - 5 u
= 230 - 5 x 5
= 230 - 25
= 205

Answer(s): 205