In a box, there are chocolate bars of 3 colours, brown, purple and grey. There are 220 more purple chocolate bars than grey chocolate bars. The number of grey chocolate bars is ²₃ more than the brown chocolate bars. Given that the number of grey chocolate bars is 30% of the total number of chocolate bars in the box, how many more purple chocolate bars are there than brown chocolate bars?

Brown chocolate bars	Purple chocolate bars	Grey chocolate bars
	1 u + 220	1 u
3x6		5x6
70%		30%
18%	52%	30%

1 + ²₃ = ³₃ + ²₃ = ⁵₃

Yellow chocolate bars : Purple chocolate bars = 3 : 5

The number of grey chocolate bars is repeated.  Make the number of grey chocolate bars the same.

5 x 6 = 30%

Total number of brown chocolate bars and purple chocolate bars in percent
= 100% - 30%
= 70%

Number of purple chocolate bars in percent
= 70% - 18%
= 52%

Number of more purple chocolate bars than grey chocolate bars in percent
= 52% - 18%
= 22%

22% = 220

1% = 220 ÷ 22 = 10

Number of more purple chocolate bars than brown chocolate bars
= 52% - 18%
= 34%
= 34 x 10
= 340

Answer(s): 340