Vanessa made 143 more cheese cupcakes than mocca cupcakes. After she gave away ⁵₇ of the cheese cupcakes and ¹₄ of the mocca cupcakes, there were an equal number of cheese cupcakes and mocca cupcakes left. How many cheese cupcakes did she give away?

	Cheese cupcakes	Mocca cupcakes	Difference
Before	7x3 = 21 u	4x2 = 8 u	13 u
Change	- 5x3 = - 15 u	- 1x2 = - 2 u
After	2x3 = 6 u	3x2 = 6 u

Fraction of cheese cupcakes left
= 1 - ⁵₇
= ²₇

Fraction of mocca cupcakes left
= 1 - ¹₄
= ³₄

The number of cheese cupcakes and mocca cupcakes in the end is the same. Make the numerators the same.  LCM of 3 and 2 is 6.

²₇ of cheese cupcakes = ³₄ of mocca cupcakes
⁶₂₁ of cheese cupcakes = ⁶₈ of mocca cupcakes

Number of more cheese cupcakes than mocca cupcakes at first
= 21 u - 8 u
= 13 u

13 u = 143

1 u = 143 ÷ 13 = 11

Number of cheese cupcakes that Vanessa gave away
= 21 u - 6 u
= 15 u
= 15 x 11
= 165

Answer(s): 165