Irene made 171 more cheese tarts than durian tarts. After she gave away ³₅ of the cheese tarts and ¹₈ of the durian tarts, there were an equal number of cheese tarts and durian tarts left. How many cheese tarts did she give away?

	Cheese tarts	Durian tarts	Difference
Before	5x7 = 35 u	8x2 = 16 u	19 u
Change	- 3x7 = - 21 u	- 1x2 = - 2 u
After	2x7 = 14 u	7x2 = 14 u

Fraction of cheese tarts left
= 1 - ³₅
= ²₅

Fraction of durian tarts left
= 1 - ¹₈
= ⁷₈

The number of cheese tarts and durian tarts in the end is the same. Make the numerators the same.  LCM of 7 and 2 is 14.

²₅ of cheese tarts = ⁷₈ of durian tarts
¹⁴₃₅ of cheese tarts = ¹⁴₁₆ of durian tarts

Number of more cheese tarts than durian tarts at first
= 35 u - 16 u
= 19 u

19 u = 171

1 u = 171 ÷ 19 = 9

Number of cheese tarts that Irene gave away
= 35 u - 14 u
= 21 u
= 21 x 9
= 189

Answer(s): 189