In a box, there are candy canes of 3 colours, yellow, purple and brown. There are 18 more purple candy canes than brown candy canes. The number of brown candy canes is ²₃ more than the yellow candy canes. Given that the number of brown candy canes is 35% of the total number of candy canes in the box, how many more purple candy canes are there than yellow candy canes?

Yellow candy canes	Purple candy canes	Brown candy canes
	1 u + 18	1 u
3x7		5x7
65%		35%
21%	44%	35%

1 + ²₃ = ³₃ + ²₃ = ⁵₃

Yellow candy canes : Purple candy canes = 3 : 5

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

5 x 7 = 35%

Total number of yellow candy canes and purple candy canes in percent
= 100% - 35%
= 65%

Number of purple candy canes in percent
= 65% - 21%
= 44%

Number of more purple candy canes than brown candy canes in percent
= 44% - 21%
= 9%

9% = 18

1% = 18 ÷ 9 = 2

Number of more purple candy canes than yellow candy canes
= 44% - 21%
= 23%
= 23 x 2
= 46

Answer(s): 46