Diana baked 50 shortbreads. ³₅ of the shortbreads were peach shortbreads. The rest were vanilla shortbreads. She gave an equal number of peach shortbreads and vanilla shortbreads away and had 3 times as many peach shortbreads as vanilla shortbreads left. How many shortbreads did she give away?

	Peach shortbreads	Vanilla shortbreads	Difference
Before	3x2 = 6 u	2x2 = 4 u	1x2 = 2 u
Change	- 3 u	- 3 u
After	3x1 = 3 u	1x1 = 1 u	2x1 = 2 u

Since Diana gave away an equal number of peach shortbreads and vanilla shortbreads, the difference in the number of peach shortbreads and vanilla shortbreads remains unchanged.  Make the difference in the peach shortbreads and vanilla shortbreads the same.  LCM of 1 and 2 is 2.

Total number of shortbreads at first
= 6 u + 4 u
= 10 u

10 u = 50

1 u = 50 ÷ 10 = 5

Number of shortbreads that Diana gave away
= 3 u + 3 u
= 6 u
= 6 x 5 
= 30

Answer(s): 30