Gwen made 204 more mocca puffs than cream puffs. After she gave away ³₇ of the mocca puffs and ¹₈ of the cream puffs, there were an equal number of mocca puffs and cream puffs left. How many mocca puffs did she give away?

	Mocca puffs	Cream puffs	Difference
Before	7x7 = 49 u	8x4 = 32 u	17 u
Change	- 3x7 = - 21 u	- 1x4 = - 4 u
After	4x7 = 28 u	7x4 = 28 u

Fraction of mocca puffs left
= 1 - ³₇
= ⁴₇

Fraction of cream puffs left
= 1 - ¹₈
= ⁷₈

The number of mocca puffs and cream puffs in the end is the same. Make the numerators the same.  LCM of 7 and 4 is 28.

⁴₇ of mocca puffs = ⁷₈ of cream puffs
²⁸₄₉ of mocca puffs = ²⁸₃₂ of cream puffs

Number of more mocca puffs than cream puffs at first
= 49 u - 32 u
= 17 u

17 u = 204

1 u = 204 ÷ 17 = 12

Number of mocca puffs that Gwen gave away
= 49 u - 28 u
= 21 u
= 21 x 12
= 252

Answer(s): 252