In a box, there are chocolate bars of 3 colours, black, red and purple. There are 175 more red chocolate bars than purple chocolate bars. The number of purple chocolate bars is ²₃ more than the black chocolate bars. Given that the number of purple chocolate bars is 25% of the total number of chocolate bars in the box, how many more red chocolate bars are there than black chocolate bars?

Black chocolate bars	Red chocolate bars	Purple chocolate bars
	1 u + 175	1 u
3x5		5x5
75%		25%
15%	60%	25%

1 + ²₃ = ³₃ + ²₃ = ⁵₃

Yellow chocolate bars : Purple chocolate bars = 3 : 5

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

5 x 5 = 25%

Total number of black chocolate bars and red chocolate bars in percent
= 100% - 25%
= 75%

Number of red chocolate bars in percent
= 75% - 15%
= 60%

Number of more red chocolate bars than purple chocolate bars in percent
= 60% - 15%
= 35%

35% = 175

1% = 175 ÷ 35 = 5

Number of more red chocolate bars than black chocolate bars
= 60% - 15%
= 45%
= 45 x 5
= 225

Answer(s): 225