Dana baked 180 cupcakes. ³₅ of the cupcakes were mango cupcakes. The rest were cherry cupcakes. She gave an equal number of mango cupcakes and cherry cupcakes away and had 5 times as many mango cupcakes as cherry cupcakes left. How many cupcakes did she give away?

	Mango cupcakes	Cherry cupcakes	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 Dana gave away an equal number of mango cupcakes and cherry cupcakes, the difference in the number of mango cupcakes and cherry cupcakes remains unchanged.  Make the difference in the mango cupcakes and cherry cupcakes the same.  LCM of 1 and 4 is 4.

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

20 u = 180

1 u = 180 ÷ 20 = 9

Number of cupcakes that Dana gave away
= 7 u + 7 u
= 14 u
= 14 x 9 
= 126

Answer(s): 126