Cathy made 14 more durian tarts than mocca tarts. After she gave away ²₇ of the durian tarts and ¹₇ of the mocca tarts, there were an equal number of durian tarts and mocca tarts left. How many durian tarts did she give away?

	Durian tarts	Mocca tarts	Difference
Before	7x6 = 42 u	7x5 = 35 u	7 u
Change	- 2x6 = - 12 u	- 1x5 = - 5 u
After	5x6 = 30 u	6x5 = 30 u

Fraction of durian tarts left
= 1 - ²₇
= ⁵₇

Fraction of mocca tarts left
= 1 - ¹₇
= ⁶₇

The number of durian tarts and mocca tarts in the end is the same. Make the numerators the same.  LCM of 6 and 5 is 30.

⁵₇ of durian tarts = ⁶₇ of mocca tarts
³⁰₄₂ of durian tarts = ³⁰₃₅ of mocca tarts

Number of more durian tarts than mocca tarts at first
= 42 u - 35 u
= 7 u

7 u = 14

1 u = 14 ÷ 7 = 2

Number of durian tarts that Cathy gave away
= 42 u - 30 u
= 12 u
= 12 x 2
= 24

Answer(s): 24