Emily made 10 more blueberry puffs than durian puffs. After she gave away ³₇ of the blueberry puffs and ¹₄ of the durian puffs, there were an equal number of blueberry puffs and durian puffs left. How many blueberry puffs did she give away?

	Blueberry puffs	Durian puffs	Difference
Before	7x3 = 21 u	4x4 = 16 u	5 u
Change	- 3x3 = - 9 u	- 1x4 = - 4 u
After	4x3 = 12 u	3x4 = 12 u

Fraction of blueberry puffs left
= 1 - ³₇
= ⁴₇

Fraction of durian puffs left
= 1 - ¹₄
= ³₄

The number of blueberry puffs and durian puffs in the end is the same. Make the numerators the same.  LCM of 3 and 4 is 12.

⁴₇ of blueberry puffs = ³₄ of durian puffs
¹²₂₁ of blueberry puffs = ¹²₁₆ of durian puffs

Number of more blueberry puffs than durian puffs at first
= 21 u - 16 u
= 5 u

5 u = 10

1 u = 10 ÷ 5 = 2

Number of blueberry puffs that Emily gave away
= 21 u - 12 u
= 9 u
= 9 x 2
= 18

Answer(s): 18