Roshel made 55 more banana cupcakes than durian cupcakes. After she gave away ²₅ of the banana cupcakes and ¹₅ of the durian cupcakes, there were an equal number of banana cupcakes and durian cupcakes left. How many banana cupcakes did she give away?

	Banana cupcakes	Durian cupcakes	Difference
Before	5x4 = 20 u	5x3 = 15 u	5 u
Change	- 2x4 = - 8 u	- 1x3 = - 3 u
After	3x4 = 12 u	4x3 = 12 u

Fraction of banana cupcakes left
= 1 - ²₅
= ³₅

Fraction of durian cupcakes left
= 1 - ¹₅
= ⁴₅

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

³₅ of banana cupcakes = ⁴₅ of durian cupcakes
¹²₂₀ of banana cupcakes = ¹²₁₅ of durian cupcakes

Number of more banana cupcakes than durian cupcakes at first
= 20 u - 15 u
= 5 u

5 u = 55

1 u = 55 ÷ 5 = 11

Number of banana cupcakes that Roshel gave away
= 20 u - 12 u
= 8 u
= 8 x 11
= 88

Answer(s): 88