Abi baked 120 macarons. ³₅ of the macarons were cherry macarons. The rest were matcha macarons. She gave an equal number of cherry macarons and matcha macarons away and had 5 times as many cherry macarons as matcha macarons left. How many macarons did she give away?

	Cherry macarons	Matcha macarons	Difference
Before	3x4 = 12 u	2x4 = 8 u	1x4 = 4 u
Change	- 7 u	- 7 u
After	5x1 = 5 u	1x1 = 1 u	4x1 = 4 u

Since Abi gave away an equal number of cherry macarons and matcha macarons, the difference in the number of cherry macarons and matcha macarons remains unchanged.  Make the difference in the cherry macarons and matcha macarons the same.  LCM of 1 and 4 is 4.

Total number of macarons at first
= 12 u + 8 u
= 20 u

20 u = 120

1 u = 120 ÷ 20 = 6

Number of macarons that Abi gave away
= 7 u + 7 u
= 14 u
= 14 x 6 
= 84

Answer(s): 84