There were some red marbles and white marbles. The marbles were packed into 2 bags. At first, Bag T contained 240 marbles and 30% of them were white marbles. Bag U contained 256 marbles and 75% of them were white marbles. How many red marbles and white marbles in total must be moved from Bag T to Bag U such that 30% of the marbles in Bag T are red and 50% of the marbles in Bag U are white?

	Bag T		Bag U
Total	240		256
	White marbles	Red marbles	White marbles	Red marbles
Before	72	168	192	64
Change	- ?	- ?	+ ?	+ ?
After	7 u	3 u	1 p	1 p

Number of white marbles in Bag T at first
= 30% x 240
= ³⁰₁₀₀ x 240
= 72

Number of red marbles in Bag T at first
= 240 - 72
= 168

Number of white marbles in Bag U at first
= 75% x 256
= ⁷⁵₁₀₀ x 256
= 192

Number of red marbles in Bag U at first
= 256 - 192
= 64

Bag T in the end
30% = ³⁰₁₀₀ =³₁₀
White marbles : Red marbles = 7 : 3

Bag U in the end
50% = ⁵⁰₁₀₀ =¹₂
White marbles : Red marbles = 1 : 1

Total number of white marbles = 7 u + 1 p

7 u + 1 p = 72 + 192
7 u + 1 p = 264 

1 p = 264 - 7 u --- (1)

Total number of red marbles = 3 u + 1 p
3 u + 1 p = 168 + 64
3 u + 1 p = 232

1 p = 232 - 3 u --- (2)

(2) = (1)
232 - 3 u = 264 - 7 u
7 u - 3 u = 264 - 232
4 u = 32

1 u = 32 ÷ 4 = 8

Total number of red marbles and white marbles that must be moved from Bag T to Bag U
= 240 - 10 u
= 240 - 10 x 8
= 240 - 80
= 160

Answer(s): 160