There were some gold cards and black cards. The cards were packed into 2 bags. At first, Box Q contained 125 cards and 40% of them were black cards. Box R contained 260 cards and 60% of them were black cards. How many gold cards and black cards in total must be moved from Box Q to Box R such that 20% of the cards in Box Q are gold and 50% of the cards in Box R are black?

	Box Q		Box R
Total	125		260
	Black cards	Gold cards	Black cards	Gold cards
Before	50	75	156	104
Change	- ?	- ?	+ ?	+ ?
After	4 u	1 u	1 p	1 p

Number of black cards in Box Q at first
= 40% x 125
= ⁴⁰₁₀₀ x 125
= 50

Number of gold cards in Box Q at first
= 125 - 50
= 75

Number of black cards in Box R at first
= 60% x 260
= ⁶⁰₁₀₀ x 260
= 156

Number of gold cards in Box R at first
= 260 - 156
= 104

Box Q in the end
20% = ²⁰₁₀₀ =¹₅
Black cards : Gold cards = 4 : 1

Box R in the end
50% = ⁵⁰₁₀₀ =¹₂
Black cards : Gold cards = 1 : 1

Total number of black cards = 4 u + 1 p

4 u + 1 p = 50 + 156
4 u + 1 p = 206 

1 p = 206 - 4 u --- (1)

Total number of gold cards = 1 u + 1 p
1 u + 1 p = 75 + 104
1 u + 1 p = 179

1 p = 179 - 1 u --- (2)

(2) = (1)
179 - 1 u = 206 - 4 u
4 u - 1 u = 206 - 179
3 u = 27

1 u = 27 ÷ 3 = 9

Total number of gold cards and black cards that must be moved from Box Q to Box R
= 125 - 5 u
= 125 - 5 x 9
= 125 - 45
= 80

Answer(s): 80