Rachel made 21 more coffee cookies than durian cookies. After she gave away ²₇ of the coffee cookies and ¹₅ of the durian cookies, there were an equal number of coffee cookies and durian cookies left. How many coffee cookies did she give away?

	Coffee cookies	Durian cookies	Difference
Before	7x4 = 28 u	5x5 = 25 u	3 u
Change	- 2x4 = - 8 u	- 1x5 = - 5 u
After	5x4 = 20 u	4x5 = 20 u

Fraction of coffee cookies left
= 1 - ²₇
= ⁵₇

Fraction of durian cookies left
= 1 - ¹₅
= ⁴₅

The number of coffee cookies and durian cookies in the end is the same. Make the numerators the same.  LCM of 4 and 5 is 20.

⁵₇ of coffee cookies = ⁴₅ of durian cookies
²⁰₂₈ of coffee cookies = ²⁰₂₅ of durian cookies

Number of more coffee cookies than durian cookies at first
= 28 u - 25 u
= 3 u

3 u = 21

1 u = 21 ÷ 3 = 7

Number of coffee cookies that Rachel gave away
= 28 u - 20 u
= 8 u
= 8 x 7
= 56

Answer(s): 56