Vanessa made 30 more apple croissants than cheese croissants. After she gave away ³₇ of the apple croissants and ¹₄ of the cheese croissants, there were an equal number of apple croissants and cheese croissants left. How many apple croissants did she give away?

	Apple croissants	Cheese croissants	Difference
Before	7x3 = 21 u	4x4 = 16 u	5 u
Change	- 3x3 = - 9 u	- 1x4 = - 4 u
After	4x3 = 12 u	3x4 = 12 u

Fraction of apple croissants left
= 1 - ³₇
= ⁴₇

Fraction of cheese croissants left
= 1 - ¹₄
= ³₄

The number of apple croissants and cheese croissants in the end is the same. Make the numerators the same.  LCM of 3 and 4 is 12.

⁴₇ of apple croissants = ³₄ of cheese croissants
¹²₂₁ of apple croissants = ¹²₁₆ of cheese croissants

Number of more apple croissants than cheese croissants at first
= 21 u - 16 u
= 5 u

5 u = 30

1 u = 30 ÷ 5 = 6

Number of apple croissants that Vanessa gave away
= 21 u - 12 u
= 9 u
= 9 x 6
= 54

Answer(s): 54