Xylia made 45 more apple macarons than cream macarons. After she gave away ⁴₇ of the apple macarons and ¹₃ of the cream macarons, there were an equal number of apple macarons and cream macarons left. How many apple macarons did she give away?

	Apple macarons	Cream macarons	Difference
Before	7x2 = 14 u	3x3 = 9 u	5 u
Change	- 4x2 = - 8 u	- 1x3 = - 3 u
After	3x2 = 6 u	2x3 = 6 u

Fraction of apple macarons left
= 1 - ⁴₇
= ³₇

Fraction of cream macarons left
= 1 - ¹₃
= ²₃

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

³₇ of apple macarons = ²₃ of cream macarons
⁶₁₄ of apple macarons = ⁶₉ of cream macarons

Number of more apple macarons than cream macarons at first
= 14 u - 9 u
= 5 u

5 u = 45

1 u = 45 ÷ 5 = 9

Number of apple macarons that Xylia gave away
= 14 u - 6 u
= 8 u
= 8 x 9
= 72

Answer(s): 72