Dana made 26 more apple macarons than mocca macarons. After she gave away ⁵₇ of the apple macarons and ¹₄ of the mocca macarons, there were an equal number of apple macarons and mocca macarons left. How many apple macarons did she give away?

	Apple macarons	Mocca macarons	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 macarons left
= 1 - ⁵₇
= ²₇

Fraction of mocca macarons left
= 1 - ¹₄
= ³₄

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

²₇ of apple macarons = ³₄ of mocca macarons
⁶₂₁ of apple macarons = ⁶₈ of mocca macarons

Number of more apple macarons than mocca macarons at first
= 21 u - 8 u
= 13 u

13 u = 26

1 u = 26 ÷ 13 = 2

Number of apple macarons that Dana gave away
= 21 u - 6 u
= 15 u
= 15 x 2
= 30

Answer(s): 30