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

Brown candy canes	Purple candy canes	Black 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 black candy canes is repeated.  Make the number of black candy canes the same.

5 x 3 = 15%

Total number of brown candy canes and purple candy canes in percent
= 100% - 15%
= 85%

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

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

58% = 406

1% = 406 ÷ 58 = 7

Number of less brown candy canes than purple candy canes
= 73% - 12%
= 61%
= 61 x 7
= 427

Answer(s): 427