Hilda made 50 more cheese puffs than coffee puffs. After she gave away ³₇ of the cheese puffs and ¹₄ of the coffee puffs, there were an equal number of cheese puffs and coffee puffs left. How many cheese puffs did she give away?

	Cheese puffs	Coffee 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 cheese puffs left
= 1 - ³₇
= ⁴₇

Fraction of coffee puffs left
= 1 - ¹₄
= ³₄

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

⁴₇ of cheese puffs = ³₄ of coffee puffs
¹²₂₁ of cheese puffs = ¹²₁₆ of coffee puffs

Number of more cheese puffs than coffee puffs at first
= 21 u - 16 u
= 5 u

5 u = 50

1 u = 50 ÷ 5 = 10

Number of cheese puffs that Hilda gave away
= 21 u - 12 u
= 9 u
= 9 x 10
= 90

Answer(s): 90