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

	Durian cookies	Cheese 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 durian cookies left
= 1 - ²₇
= ⁵₇

Fraction of cheese cookies left
= 1 - ¹₅
= ⁴₅

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

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

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

3 u = 15

1 u = 15 ÷ 3 = 5

Number of durian cookies that Olivia gave away
= 28 u - 20 u
= 8 u
= 8 x 5
= 40

Answer(s): 40