Erika made 65 more strawberry shortbreads than apple shortbreads. After she gave away ⁵₇ of the strawberry shortbreads and ¹₄ of the apple shortbreads, there were an equal number of strawberry shortbreads and apple shortbreads left. How many strawberry shortbreads did she give away?

	Strawberry shortbreads	Apple shortbreads	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 strawberry shortbreads left
= 1 - ⁵₇
= ²₇

Fraction of apple shortbreads left
= 1 - ¹₄
= ³₄

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

²₇ of strawberry shortbreads = ³₄ of apple shortbreads
⁶₂₁ of strawberry shortbreads = ⁶₈ of apple shortbreads

Number of more strawberry shortbreads than apple shortbreads at first
= 21 u - 8 u
= 13 u

13 u = 65

1 u = 65 ÷ 13 = 5

Number of strawberry shortbreads that Erika gave away
= 21 u - 6 u
= 15 u
= 15 x 5
= 75

Answer(s): 75