Ivory made 40 more apple muffins than blueberry muffins. After she gave away ⁴₇ of the apple muffins and ¹₃ of the blueberry muffins, there were an equal number of apple muffins and blueberry muffins left. How many apple muffins did she give away?

	Apple muffins	Blueberry muffins	Difference
Before	7x2 = 14 u	3x3 = 9 u	5 u
Change	- 4x2 = - 8 u	- 1x3 = - 3 u
After	3x2 = 6 u	2x3 = 6 u

Fraction of apple muffins left
= 1 - ⁴₇
= ³₇

Fraction of blueberry muffins left
= 1 - ¹₃
= ²₃

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

³₇ of apple muffins = ²₃ of blueberry muffins
⁶₁₄ of apple muffins = ⁶₉ of blueberry muffins

Number of more apple muffins than blueberry muffins at first
= 14 u - 9 u
= 5 u

5 u = 40

1 u = 40 ÷ 5 = 8

Number of apple muffins that Ivory gave away
= 14 u - 6 u
= 8 u
= 8 x 8
= 64

Answer(s): 64