There were some grey beads and green beads. The beads were packed into 2 bags. At first, Box P contained 190 beads and 10% of them were green beads. Box Q contained 324 beads and 75% of them were green beads. How many grey beads and green beads in total must be moved from Box P to Box Q such that 25% of the beads in Box P are grey and 50% of the beads in Box Q are green?

	Box P		Box Q
Total	190		324
	Green beads	Grey beads	Green beads	Grey beads
Before	19	171	243	81
Change	- ?	- ?	+ ?	+ ?
After	3 u	1 u	1 p	1 p

Number of green beads in Box P at first
= 10% x 190
= ¹⁰₁₀₀ x 190
= 19

Number of grey beads in Box P at first
= 190 - 19
= 171

Number of green beads in Box Q at first
= 75% x 324
= ⁷⁵₁₀₀ x 324
= 243

Number of grey beads in Box Q at first
= 324 - 243
= 81

Box P in the end
25% = ²⁵₁₀₀ =¹₄
Green beads : Grey beads = 3 : 1

Box Q in the end
50% = ⁵⁰₁₀₀ =¹₂
Green beads : Grey beads = 1 : 1

Total number of green beads = 3 u + 1 p

3 u + 1 p = 19 + 243
3 u + 1 p = 262 

1 p = 262 - 3 u --- (1)

Total number of grey beads = 1 u + 1 p
1 u + 1 p = 171 + 81
1 u + 1 p = 252

1 p = 252 - 1 u --- (2)

(2) = (1)
252 - 1 u = 262 - 3 u
3 u - 1 u = 262 - 252
2 u = 10

1 u = 10 ÷ 2 = 5

Total number of grey beads and green beads that must be moved from Box P to Box Q
= 190 - 4 u
= 190 - 4 x 5
= 190 - 20
= 170

Answer(s): 170