There were some yellow cards and pink cards. The cards were packed into 2 bags. At first, Box Y contained 120 cards and 40% of them were pink cards. Box Z contained 60 cards and 80% of them were pink cards. How many yellow cards and pink cards in total must be moved from Box Y to Box Z such that 20% of the cards in Box Y are yellow and 50% of the cards in Box Z are pink?

	Box Y		Box Z
Total	120		60
	Pink cards	Yellow cards	Pink cards	Yellow cards
Before	48	72	48	12
Change	- ?	- ?	+ ?	+ ?
After	4 u	1 u	1 p	1 p

Number of pink cards in Box Y at first
= 40% x 120
= ⁴⁰₁₀₀ x 120
= 48

Number of yellow cards in Box Y at first
= 120 - 48
= 72

Number of pink cards in Box Z at first
= 80% x 60
= ⁸⁰₁₀₀ x 60
= 48

Number of yellow cards in Box Z at first
= 60 - 48
= 12

Box Y in the end
20% = ²⁰₁₀₀ =¹₅
Pink cards : Yellow cards = 4 : 1

Box Z in the end
50% = ⁵⁰₁₀₀ =¹₂
Pink cards : Yellow cards = 1 : 1

Total number of pink cards = 4 u + 1 p

4 u + 1 p = 48 + 48
4 u + 1 p = 96 

1 p = 96 - 4 u --- (1)

Total number of yellow cards = 1 u + 1 p
1 u + 1 p = 72 + 12
1 u + 1 p = 84

1 p = 84 - 1 u --- (2)

(2) = (1)
84 - 1 u = 96 - 4 u
4 u - 1 u = 96 - 84
3 u = 12

1 u = 12 ÷ 3 = 4

Total number of yellow cards and pink cards that must be moved from Box Y to Box Z
= 120 - 5 u
= 120 - 5 x 4
= 120 - 20
= 100

Answer(s): 100