In a box, there are candy canes of 3 colours, blue, grey and purple. There are 406 more grey candy canes than purple candy canes. The number of purple candy canes is ¹₄ more than the blue candy canes. Given that the number of purple candy canes is 15% of the total number of candy canes in the box, how many more grey candy canes are there than blue candy canes?

Blue candy canes	Grey candy canes	Purple candy canes
	1 u + 406	1 u
4x3		5x3
85%		15%
12%	73%	15%

1 + ¹₄ = ⁴₄ + ¹₄ = ⁵₄

Yellow candy canes : Purple candy canes = 4 : 5

The number of purple candy canes is repeated.  Make the number of purple candy canes the same.

5 x 3 = 15%

Total number of blue candy canes and grey candy canes in percent
= 100% - 15%
= 85%

Number of grey candy canes in percent
= 85% - 12%
= 73%

Number of more grey candy canes than purple candy canes in percent
= 73% - 12%
= 58%

58% = 406

1% = 406 ÷ 58 = 7

Number of more grey candy canes than blue candy canes
= 73% - 12%
= 61%
= 61 x 7
= 427

Answer(s): 427