There were some blue stickers and purple stickers. The stickers were packed into 2 bags. At first, Bag S contained 140 stickers and 40% of them were purple stickers. Bag T contained 112 stickers and 75% of them were purple stickers. How many blue stickers and purple stickers in total must be moved from Bag S to Bag T such that 30% of the stickers in Bag S are blue and 50% of the stickers in Bag T are purple?

	Bag S		Bag T
Total	140		112
	Purple stickers	Blue stickers	Purple stickers	Blue stickers
Before	56	84	84	28
Change	- ?	- ?	+ ?	+ ?
After	7 u	3 u	1 p	1 p

Number of purple stickers in Bag S at first
= 40% x 140
= ⁴⁰₁₀₀ x 140
= 56

Number of blue stickers in Bag S at first
= 140 - 56
= 84

Number of purple stickers in Bag T at first
= 75% x 112
= ⁷⁵₁₀₀ x 112
= 84

Number of blue stickers in Bag T at first
= 112 - 84
= 28

Bag S in the end
30% = ³⁰₁₀₀ =³₁₀
Purple stickers : Blue stickers = 7 : 3

Bag T in the end
50% = ⁵⁰₁₀₀ =¹₂
Purple stickers : Blue stickers = 1 : 1

Total number of purple stickers = 7 u + 1 p

7 u + 1 p = 56 + 84
7 u + 1 p = 140 

1 p = 140 - 7 u --- (1)

Total number of blue stickers = 3 u + 1 p
3 u + 1 p = 84 + 28
3 u + 1 p = 112

1 p = 112 - 3 u --- (2)

(2) = (1)
112 - 3 u = 140 - 7 u
7 u - 3 u = 140 - 112
4 u = 28

1 u = 28 ÷ 4 = 7

Total number of blue stickers and purple stickers that must be moved from Bag S to Bag T
= 140 - 10 u
= 140 - 10 x 7
= 140 - 70
= 70

Answer(s): 70