There were some blue erasers and black erasers. The erasers were packed into 2 bags. At first, Box A contained 240 erasers and 30% of them were black erasers. Box B contained 200 erasers and 80% of them were black erasers. How many blue erasers and black erasers in total must be moved from Box A to Box B such that 30% of the erasers in Box A are blue and 50% of the erasers in Box B are black?

	Box A		Box B
Total	240		200
	Black erasers	Blue erasers	Black erasers	Blue erasers
Before	72	168	160	40
Change	- ?	- ?	+ ?	+ ?
After	7 u	3 u	1 p	1 p

Number of black erasers in Box A at first
= 30% x 240
= ³⁰₁₀₀ x 240
= 72

Number of blue erasers in Box A at first
= 240 - 72
= 168

Number of black erasers in Box B at first
= 80% x 200
= ⁸⁰₁₀₀ x 200
= 160

Number of blue erasers in Box B at first
= 200 - 160
= 40

Box A in the end
30% = ³⁰₁₀₀ =³₁₀
Black erasers : Blue erasers = 7 : 3

Box B in the end
50% = ⁵⁰₁₀₀ =¹₂
Black erasers : Blue erasers = 1 : 1

Total number of black erasers = 7 u + 1 p

7 u + 1 p = 72 + 160
7 u + 1 p = 232 

1 p = 232 - 7 u --- (1)

Total number of blue erasers = 3 u + 1 p
3 u + 1 p = 168 + 40
3 u + 1 p = 208

1 p = 208 - 3 u --- (2)

(2) = (1)
208 - 3 u = 232 - 7 u
7 u - 3 u = 232 - 208
4 u = 24

1 u = 24 ÷ 4 = 6

Total number of blue erasers and black erasers that must be moved from Box A to Box B
= 240 - 10 u
= 240 - 10 x 6
= 240 - 60
= 180

Answer(s): 180