Xandra made 161 more blueberry macarons than banana macarons. After she gave away ⁵₇ of the blueberry macarons and ¹₆ of the banana macarons, there were an equal number of blueberry macarons and banana macarons left. How many blueberry macarons did she give away?

	Blueberry macarons	Banana macarons	Difference
Before	7x5 = 35 u	6x2 = 12 u	23 u
Change	- 5x5 = - 25 u	- 1x2 = - 2 u
After	2x5 = 10 u	5x2 = 10 u

Fraction of blueberry macarons left
= 1 - ⁵₇
= ²₇

Fraction of banana macarons left
= 1 - ¹₆
= ⁵₆

The number of blueberry macarons and banana macarons in the end is the same. Make the numerators the same.  LCM of 5 and 2 is 10.

²₇ of blueberry macarons = ⁵₆ of banana macarons
¹⁰₃₅ of blueberry macarons = ¹⁰₁₂ of banana macarons

Number of more blueberry macarons than banana macarons at first
= 35 u - 12 u
= 23 u

23 u = 161

1 u = 161 ÷ 23 = 7

Number of blueberry macarons that Xandra gave away
= 35 u - 10 u
= 25 u
= 25 x 7
= 175

Answer(s): 175