There were some gold marbles and pink marbles. The marbles were packed into 2 bags. At first, Bag U contained 150 marbles and 40% of them were pink marbles. Bag V contained 72 marbles and 75% of them were pink marbles. How many gold marbles and pink marbles in total must be moved from Bag U to Bag V such that 20% of the marbles in Bag U are gold and 50% of the marbles in Bag V are pink?

	Bag U		Bag V
Total	150		72
	Pink marbles	Gold marbles	Pink marbles	Gold marbles
Before	60	90	54	18
Change	- ?	- ?	+ ?	+ ?
After	4 u	1 u	1 p	1 p

Number of pink marbles in Bag U at first
= 40% x 150
= ⁴⁰₁₀₀ x 150
= 60

Number of gold marbles in Bag U at first
= 150 - 60
= 90

Number of pink marbles in Bag V at first
= 75% x 72
= ⁷⁵₁₀₀ x 72
= 54

Number of gold marbles in Bag V at first
= 72 - 54
= 18

Bag U in the end
20% = ²⁰₁₀₀ =¹₅
Pink marbles : Gold marbles = 4 : 1

Bag V in the end
50% = ⁵⁰₁₀₀ =¹₂
Pink marbles : Gold marbles = 1 : 1

Total number of pink marbles = 4 u + 1 p

4 u + 1 p = 60 + 54
4 u + 1 p = 114 

1 p = 114 - 4 u --- (1)

Total number of gold marbles = 1 u + 1 p
1 u + 1 p = 90 + 18
1 u + 1 p = 108

1 p = 108 - 1 u --- (2)

(2) = (1)
108 - 1 u = 114 - 4 u
4 u - 1 u = 114 - 108
3 u = 6

1 u = 6 ÷ 3 = 2

Total number of gold marbles and pink marbles that must be moved from Bag U to Bag V
= 150 - 5 u
= 150 - 5 x 2
= 150 - 10
= 140

Answer(s): 140