There were some white erasers and pink erasers. The erasers were packed into 2 bags. At first, Box Q contained 160 erasers and 30% of them were pink erasers. Box R contained 365 erasers and 60% of them were pink erasers. How many white erasers and pink erasers in total must be moved from Box Q to Box R such that 20% of the erasers in Box Q are white and 50% of the erasers in Box R are pink?

	Box Q		Box R
Total	160		365
	Pink erasers	White erasers	Pink erasers	White erasers
Before	48	112	219	146
Change	- ?	- ?	+ ?	+ ?
After	4 u	1 u	1 p	1 p

Number of pink erasers in Box Q at first
= 30% x 160
= ³⁰₁₀₀ x 160
= 48

Number of white erasers in Box Q at first
= 160 - 48
= 112

Number of pink erasers in Box R at first
= 60% x 365
= ⁶⁰₁₀₀ x 365
= 219

Number of white erasers in Box R at first
= 365 - 219
= 146

Box Q in the end
20% = ²⁰₁₀₀ =¹₅
Pink erasers : White erasers = 4 : 1

Box R in the end
50% = ⁵⁰₁₀₀ =¹₂
Pink erasers : White erasers = 1 : 1

Total number of pink erasers = 4 u + 1 p

4 u + 1 p = 48 + 219
4 u + 1 p = 267 

1 p = 267 - 4 u --- (1)

Total number of white erasers = 1 u + 1 p
1 u + 1 p = 112 + 146
1 u + 1 p = 258

1 p = 258 - 1 u --- (2)

(2) = (1)
258 - 1 u = 267 - 4 u
4 u - 1 u = 267 - 258
3 u = 9

1 u = 9 ÷ 3 = 3

Total number of white erasers and pink erasers that must be moved from Box Q to Box R
= 160 - 5 u
= 160 - 5 x 3
= 160 - 15
= 145

Answer(s): 145