Xylia made 42 more strawberry macarons than banana macarons. After she gave away ²₅ of the strawberry macarons and ¹₆ of the banana macarons, there were an equal number of strawberry macarons and banana macarons left. How many strawberry macarons did she give away?

	Strawberry macarons	Banana macarons	Difference
Before	5x5 = 25 u	6x3 = 18 u	7 u
Change	- 2x5 = - 10 u	- 1x3 = - 3 u
After	3x5 = 15 u	5x3 = 15 u

Fraction of strawberry macarons left
= 1 - ²₅
= ³₅

Fraction of banana macarons left
= 1 - ¹₆
= ⁵₆

The number of strawberry macarons and banana macarons in the end is the same. Make the numerators the same.  LCM of 5 and 3 is 15.

³₅ of strawberry macarons = ⁵₆ of banana macarons
¹⁵₂₅ of strawberry macarons = ¹⁵₁₈ of banana macarons

Number of more strawberry macarons than banana macarons at first
= 25 u - 18 u
= 7 u

7 u = 42

1 u = 42 ÷ 7 = 6

Number of strawberry macarons that Xylia gave away
= 25 u - 15 u
= 10 u
= 10 x 6
= 60

Answer(s): 60