There were some yellow cards and gold cards. The cards were packed into 2 bags. At first, Bag H contained 130 cards and 40% of them were gold cards. Bag J contained 270 cards and 60% of them were gold cards. How many yellow cards and gold cards in total must be moved from Bag H to Bag J such that 25% of the cards in Bag H are yellow and 50% of the cards in Bag J are gold?

	Bag H		Bag J
Total	130		270
	Gold cards	Yellow cards	Gold cards	Yellow cards
Before	52	78	162	108
Change	- ?	- ?	+ ?	+ ?
After	3 u	1 u	1 p	1 p

Number of gold cards in Bag H at first
= 40% x 130
= ⁴⁰₁₀₀ x 130
= 52

Number of yellow cards in Bag H at first
= 130 - 52
= 78

Number of gold cards in Bag J at first
= 60% x 270
= ⁶⁰₁₀₀ x 270
= 162

Number of yellow cards in Bag J at first
= 270 - 162
= 108

Bag H in the end
25% = ²⁵₁₀₀ =¹₄
Gold cards : Yellow cards = 3 : 1

Bag J in the end
50% = ⁵⁰₁₀₀ =¹₂
Gold cards : Yellow cards = 1 : 1

Total number of gold cards = 3 u + 1 p

3 u + 1 p = 52 + 162
3 u + 1 p = 214 

1 p = 214 - 3 u --- (1)

Total number of yellow cards = 1 u + 1 p
1 u + 1 p = 78 + 108
1 u + 1 p = 186

1 p = 186 - 1 u --- (2)

(2) = (1)
186 - 1 u = 214 - 3 u
3 u - 1 u = 214 - 186
2 u = 28

1 u = 28 ÷ 2 = 14

Total number of yellow cards and gold cards that must be moved from Bag H to Bag J
= 130 - 4 u
= 130 - 4 x 14
= 130 - 56
= 74

Answer(s): 74