In a container, there are lollipops of 3 colours, purple, yellow and gold. There are 469 less gold lollipops than yellow lollipops. The number of gold lollipops is ¹₃ more than the purple lollipops. Given that the number of gold lollipops is 12% of the total number of lollipops in the container, how many less purple lollipops are there than yellow lollipops?

Purple lollipops	Yellow lollipops	Gold lollipops
	1 u + 469	1 u
3x3		4x3
88%		12%
9%	79%	12%

1 + ¹₃ = ³₃ + ¹₃ = ⁴₃

Yellow lollipops : Purple lollipops = 3 : 4

The number of gold lollipops is repeated.  Make the number of gold lollipops the same.

4 x 3 = 12%

Total number of purple lollipops and yellow lollipops in percent
= 100% - 12%
= 88%

Number of yellow lollipops in percent
= 88% - 9%
= 79%

Number of more yellow lollipops than gold lollipops in percent
= 79% - 9%
= 67%

67% = 469

1% = 469 ÷ 67 = 7

Number of less purple lollipops than yellow lollipops
= 79% - 9%
= 70%
= 70 x 7
= 490

Answer(s): 490