Gabby made 44 more mocca cupcakes than durian cupcakes. After she gave away ²₅ of the mocca cupcakes and ¹₈ of the durian cupcakes, there were an equal number of mocca cupcakes and durian cupcakes left. How many mocca cupcakes did she give away?

	Mocca cupcakes	Durian cupcakes	Difference
Before	5x7 = 35 u	8x3 = 24 u	11 u
Change	- 2x7 = - 14 u	- 1x3 = - 3 u
After	3x7 = 21 u	7x3 = 21 u

Fraction of mocca cupcakes left
= 1 - ²₅
= ³₅

Fraction of durian cupcakes left
= 1 - ¹₈
= ⁷₈

The number of mocca cupcakes and durian cupcakes in the end is the same. Make the numerators the same.  LCM of 7 and 3 is 21.

³₅ of mocca cupcakes = ⁷₈ of durian cupcakes
²¹₃₅ of mocca cupcakes = ²¹₂₄ of durian cupcakes

Number of more mocca cupcakes than durian cupcakes at first
= 35 u - 24 u
= 11 u

11 u = 44

1 u = 44 ÷ 11 = 4

Number of mocca cupcakes that Gabby gave away
= 35 u - 21 u
= 14 u
= 14 x 4
= 56

Answer(s): 56