Raeann made 52 more apple cupcakes than pandan cupcakes. After she gave away ⁵₇ of the apple cupcakes and ¹₄ of the pandan cupcakes, there were an equal number of apple cupcakes and pandan cupcakes left. How many apple cupcakes did she give away?

	Apple cupcakes	Pandan cupcakes	Difference
Before	7x3 = 21 u	4x2 = 8 u	13 u
Change	- 5x3 = - 15 u	- 1x2 = - 2 u
After	2x3 = 6 u	3x2 = 6 u

Fraction of apple cupcakes left
= 1 - ⁵₇
= ²₇

Fraction of pandan cupcakes left
= 1 - ¹₄
= ³₄

The number of apple cupcakes and pandan cupcakes in the end is the same. Make the numerators the same.  LCM of 3 and 2 is 6.

²₇ of apple cupcakes = ³₄ of pandan cupcakes
⁶₂₁ of apple cupcakes = ⁶₈ of pandan cupcakes

Number of more apple cupcakes than pandan cupcakes at first
= 21 u - 8 u
= 13 u

13 u = 52

1 u = 52 ÷ 13 = 4

Number of apple cupcakes that Raeann gave away
= 21 u - 6 u
= 15 u
= 15 x 4
= 60

Answer(s): 60