There were some blue beads and silver beads. The beads were packed into 2 bags. At first, Box P contained 115 beads and 40% of them were silver beads. Box Q contained 145 beads and 60% of them were silver beads. How many blue beads and silver beads in total must be moved from Box P to Box Q such that 25% of the beads in Box P are blue and 50% of the beads in Box Q are silver?

	Box P		Box Q
Total	115		145
	Silver beads	Blue beads	Silver beads	Blue beads
Before	46	69	87	58
Change	- ?	- ?	+ ?	+ ?
After	3 u	1 u	1 p	1 p

Number of silver beads in Box P at first
= 40% x 115
= ⁴⁰₁₀₀ x 115
= 46

Number of blue beads in Box P at first
= 115 - 46
= 69

Number of silver beads in Box Q at first
= 60% x 145
= ⁶⁰₁₀₀ x 145
= 87

Number of blue beads in Box Q at first
= 145 - 87
= 58

Box P in the end
25% = ²⁵₁₀₀ =¹₄
Silver beads : Blue beads = 3 : 1

Box Q in the end
50% = ⁵⁰₁₀₀ =¹₂
Silver beads : Blue beads = 1 : 1

Total number of silver beads = 3 u + 1 p

3 u + 1 p = 46 + 87
3 u + 1 p = 133 

1 p = 133 - 3 u --- (1)

Total number of blue beads = 1 u + 1 p
1 u + 1 p = 69 + 58
1 u + 1 p = 127

1 p = 127 - 1 u --- (2)

(2) = (1)
127 - 1 u = 133 - 3 u
3 u - 1 u = 133 - 127
2 u = 6

1 u = 6 ÷ 2 = 3

Total number of blue beads and silver beads that must be moved from Box P to Box Q
= 115 - 4 u
= 115 - 4 x 3
= 115 - 12
= 103

Answer(s): 103