There were some black beads and red beads. The beads were packed into 2 bags. At first, Bag P contained 280 beads and 30% of them were red beads. Bag Q contained 304 beads and 75% of them were red beads. How many black beads and red beads in total must be moved from Bag P to Bag Q such that 30% of the beads in Bag P are black and 50% of the beads in Bag Q are red?

	Bag P		Bag Q
Total	280		304
	Red beads	Black beads	Red beads	Black beads
Before	84	196	228	76
Change	- ?	- ?	+ ?	+ ?
After	7 u	3 u	1 p	1 p

Number of red beads in Bag P at first
= 30% x 280
= ³⁰₁₀₀ x 280
= 84

Number of black beads in Bag P at first
= 280 - 84
= 196

Number of red beads in Bag Q at first
= 75% x 304
= ⁷⁵₁₀₀ x 304
= 228

Number of black beads in Bag Q at first
= 304 - 228
= 76

Bag P in the end
30% = ³⁰₁₀₀ =³₁₀
Red beads : Black beads = 7 : 3

Bag Q in the end
50% = ⁵⁰₁₀₀ =¹₂
Red beads : Black beads = 1 : 1

Total number of red beads = 7 u + 1 p

7 u + 1 p = 84 + 228
7 u + 1 p = 312 

1 p = 312 - 7 u --- (1)

Total number of black beads = 3 u + 1 p
3 u + 1 p = 196 + 76
3 u + 1 p = 272

1 p = 272 - 3 u --- (2)

(2) = (1)
272 - 3 u = 312 - 7 u
7 u - 3 u = 312 - 272
4 u = 40

1 u = 40 ÷ 4 = 10

Total number of black beads and red beads that must be moved from Bag P to Bag Q
= 280 - 10 u
= 280 - 10 x 10
= 280 - 100
= 180

Answer(s): 180