There were some green cards and gold cards. The cards were packed into 2 bags. At first, Bag T contained 190 cards and 30% of them were gold cards. Bag U contained 200 cards and 75% of them were gold cards. How many green cards and gold cards in total must be moved from Bag T to Bag U such that 20% of the cards in Bag T are green and 50% of the cards in Bag U are gold?

	Bag T		Bag U
Total	190		200
	Gold cards	Green cards	Gold cards	Green cards
Before	57	133	150	50
Change	- ?	- ?	+ ?	+ ?
After	4 u	1 u	1 p	1 p

Number of gold cards in Bag T at first
= 30% x 190
= ³⁰₁₀₀ x 190
= 57

Number of green cards in Bag T at first
= 190 - 57
= 133

Number of gold cards in Bag U at first
= 75% x 200
= ⁷⁵₁₀₀ x 200
= 150

Number of green cards in Bag U at first
= 200 - 150
= 50

Bag T in the end
20% = ²⁰₁₀₀ =¹₅
Gold cards : Green cards = 4 : 1

Bag U in the end
50% = ⁵⁰₁₀₀ =¹₂
Gold cards : Green cards = 1 : 1

Total number of gold cards = 4 u + 1 p

4 u + 1 p = 57 + 150
4 u + 1 p = 207 

1 p = 207 - 4 u --- (1)

Total number of green cards = 1 u + 1 p
1 u + 1 p = 133 + 50
1 u + 1 p = 183

1 p = 183 - 1 u --- (2)

(2) = (1)
183 - 1 u = 207 - 4 u
4 u - 1 u = 207 - 183
3 u = 24

1 u = 24 ÷ 3 = 8

Total number of green cards and gold cards that must be moved from Bag T to Bag U
= 190 - 5 u
= 190 - 5 x 8
= 190 - 40
= 150

Answer(s): 150