Marion made 52 more mocca muffins than banana muffins. After she gave away ⁵₇ of the mocca muffins and ¹₄ of the banana muffins, there were an equal number of mocca muffins and banana muffins left. How many mocca muffins did she give away?

	Mocca muffins	Banana muffins	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 mocca muffins left
= 1 - ⁵₇
= ²₇

Fraction of banana muffins left
= 1 - ¹₄
= ³₄

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

²₇ of mocca muffins = ³₄ of banana muffins
⁶₂₁ of mocca muffins = ⁶₈ of banana muffins

Number of more mocca muffins than banana muffins at first
= 21 u - 8 u
= 13 u

13 u = 52

1 u = 52 ÷ 13 = 4

Number of mocca muffins that Marion gave away
= 21 u - 6 u
= 15 u
= 15 x 4
= 60

Answer(s): 60