Emily made 15 more blueberry tarts than mocca tarts. After she gave away ²₇ of the blueberry tarts and ¹₅ of the mocca tarts, there were an equal number of blueberry tarts and mocca tarts left. How many blueberry tarts did she give away?

	Blueberry tarts	Mocca tarts	Difference
Before	7x4 = 28 u	5x5 = 25 u	3 u
Change	- 2x4 = - 8 u	- 1x5 = - 5 u
After	5x4 = 20 u	4x5 = 20 u

Fraction of blueberry tarts left
= 1 - ²₇
= ⁵₇

Fraction of mocca tarts left
= 1 - ¹₅
= ⁴₅

The number of blueberry tarts and mocca tarts in the end is the same. Make the numerators the same.  LCM of 4 and 5 is 20.

⁵₇ of blueberry tarts = ⁴₅ of mocca tarts
²⁰₂₈ of blueberry tarts = ²⁰₂₅ of mocca tarts

Number of more blueberry tarts than mocca tarts at first
= 28 u - 25 u
= 3 u

3 u = 15

1 u = 15 ÷ 3 = 5

Number of blueberry tarts that Emily gave away
= 28 u - 20 u
= 8 u
= 8 x 5
= 40

Answer(s): 40