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

	Mocha cupcakes	Vanilla 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 Yen gave away an equal number of mocha cupcakes and vanilla cupcakes, the difference in the number of mocha cupcakes and vanilla cupcakes remains unchanged.  Make the difference in the mocha cupcakes and vanilla 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 Yen gave away
= 7 u + 7 u
= 14 u
= 14 x 9 
= 126

Answer(s): 126