Jean made 231 more apple cupcakes than mocca cupcakes. After she gave away ⁵₇ of the apple cupcakes and ¹₈ of the mocca cupcakes, there were an equal number of apple cupcakes and mocca cupcakes left. How many apple cupcakes did she give away?

	Apple 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 apple cupcakes left
= 1 - ⁵₇
= ²₇

Fraction of mocca cupcakes left
= 1 - ¹₈
= ⁷₈

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

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

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

33 u = 231

1 u = 231 ÷ 33 = 7

Number of apple cupcakes that Jean gave away
= 49 u - 14 u
= 35 u
= 35 x 7
= 245

Answer(s): 245