Victoria made 39 more coffee cupcakes than durian cupcakes. After she gave away ⁴₇ of the coffee cupcakes and ¹₅ of the durian cupcakes, there were an equal number of coffee cupcakes and durian cupcakes left. How many coffee cupcakes did she give away?

	Coffee cupcakes	Durian cupcakes	Difference
Before	7x4 = 28 u	5x3 = 15 u	13 u
Change	- 4x4 = - 16 u	- 1x3 = - 3 u
After	3x4 = 12 u	4x3 = 12 u

Fraction of coffee cupcakes left
= 1 - ⁴₇
= ³₇

Fraction of durian cupcakes left
= 1 - ¹₅
= ⁴₅

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

³₇ of coffee cupcakes = ⁴₅ of durian cupcakes
¹²₂₈ of coffee cupcakes = ¹²₁₅ of durian cupcakes

Number of more coffee cupcakes than durian cupcakes at first
= 28 u - 15 u
= 13 u

13 u = 39

1 u = 39 ÷ 13 = 3

Number of coffee cupcakes that Victoria gave away
= 28 u - 12 u
= 16 u
= 16 x 3
= 48

Answer(s): 48