Rachel made 20 more blueberry cookies than cream cookies. After she gave away ²₅ of the blueberry cookies and ¹₅ of the cream cookies, there were an equal number of blueberry cookies and cream cookies left. How many blueberry cookies did she give away?

	Blueberry cookies	Cream cookies	Difference
Before	5x4 = 20 u	5x3 = 15 u	5 u
Change	- 2x4 = - 8 u	- 1x3 = - 3 u
After	3x4 = 12 u	4x3 = 12 u

Fraction of blueberry cookies left
= 1 - ²₅
= ³₅

Fraction of cream cookies left
= 1 - ¹₅
= ⁴₅

The number of blueberry cookies and cream cookies in the end is the same. Make the numerators the same.  LCM of 4 and 3 is 12.

³₅ of blueberry cookies = ⁴₅ of cream cookies
¹²₂₀ of blueberry cookies = ¹²₁₅ of cream cookies

Number of more blueberry cookies than cream cookies at first
= 20 u - 15 u
= 5 u

5 u = 20

1 u = 20 ÷ 5 = 4

Number of blueberry cookies that Rachel gave away
= 20 u - 12 u
= 8 u
= 8 x 4
= 32

Answer(s): 32