Julie used ⁵₇ of her yellow stickers and ³₄ of her purple stickers to decorate her diary. In the end, she had an equal number of yellow stickers and purple stickers left. Given that Julie had a total of 180 yellow and purple stickers at first, how many purple stickers did she use to decorate the diary?

	Yellow stickers	Purple stickers
Before	7x1 = 7 u	4x2 = 8 u
Change	- 5x1 = - 5 u	- 3x2 = - 6 u
After	2x1 = 2 u	1x2 = 2 u

The number of yellow stickers and purple stickers in the end is the same.  Make the number of yellow stickers and purple stickers in the end the same.  LCM of 2 and 1 is 2.

Total number of stickers that Julie used to decorate the diary
= 7 u + 8 u
= 15 u

15 u = 180

1 u = 180 ÷ 15 = 12

Number of purple stickers that Julie used to decorate the diary
= 6 u
= 6 x 12
= 72

Answer(s): 72