Hazel made 132 more durian cupcakes than mocca cupcakes. After she gave away ⁵₇ of the durian cupcakes and ¹₈ of the mocca cupcakes, there were an equal number of durian cupcakes and mocca cupcakes left. How many durian cupcakes did she give away?

	Durian cupcakes	Mocca cupcakes	Difference
Before	7x7 = 49 u	8x2 = 16 u	33 u
Change	- 5x7 = - 35 u	- 1x2 = - 2 u
After	2x7 = 14 u	7x2 = 14 u

Fraction of durian cupcakes left
= 1 - ⁵₇
= ²₇

Fraction of mocca cupcakes left
= 1 - ¹₈
= ⁷₈

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

²₇ of durian cupcakes = ⁷₈ of mocca cupcakes
¹⁴₄₉ of durian cupcakes = ¹⁴₁₆ of mocca cupcakes

Number of more durian cupcakes than mocca cupcakes at first
= 49 u - 16 u
= 33 u

33 u = 132

1 u = 132 ÷ 33 = 4

Number of durian cupcakes that Hazel gave away
= 49 u - 14 u
= 35 u
= 35 x 4
= 140

Answer(s): 140