Box P contains 2 yellow beads and 4 black beads. Box Q contains 73 yellow beads and 20 black beads. How many black beads and yellow beads must be moved from Box Q to put into Box P so that 50% of the beads in Box A are yellow and 80% of the beads in Box Q are yellow?

	Box P		Box Q
	Yellow beads	Black beads	Yellow beads	Black beads
Before	2	4	73	20
Change	+ ?	+ ?	- ?	- ?
After	1 u	1 u	4 p	1 p

50% = ⁵⁰₁₀₀ = 12

80% = ⁸⁰₁₀₀ = 45

Number of yellow beads = 2 + 73 = 75 

Number of black beads = 4 + 20 = 24 

1 u + 4 p = 75 --- (1)

1 u + 1 p = 24 ---(2)

(1) - (2)
(1 u + 4 p) - (1 u + 1 p) = 75 - 24
4 p - 1 p = 51
3 p = 51

1 p = 51 ÷ 3 = 17

From (2):
1 u + 1 p = 24
1 u + 1 x 17 = 24
1 u + 17 = 24

1 u = 24 - 17 = 7

Number of black beads to be moved from Box Q to Box P
= 20 - 1 p
= 20 - 1 x 17
= 20 - 17
= 3

Number of yellow beads to be moved from Box Q to Box P
= 1 u - 2
= 7 - 2
= 5

Total number of black and yellow beads to be moved from Box Q to Box P
= 3 + 5
= 8

Answer(s): 8