Gem made 21 more cheese tarts than blueberry tarts. After she gave away ²₇ of the cheese tarts and ¹₇ of the blueberry tarts, there were an equal number of cheese tarts and blueberry tarts left. How many cheese tarts did she give away?

	Cheese tarts	Blueberry tarts	Difference
Before	7x6 = 42 u	7x5 = 35 u	7 u
Change	- 2x6 = - 12 u	- 1x5 = - 5 u
After	5x6 = 30 u	6x5 = 30 u

Fraction of cheese tarts left
= 1 - ²₇
= ⁵₇

Fraction of blueberry tarts left
= 1 - ¹₇
= ⁶₇

The number of cheese tarts and blueberry tarts in the end is the same. Make the numerators the same.  LCM of 6 and 5 is 30.

⁵₇ of cheese tarts = ⁶₇ of blueberry tarts
³⁰₄₂ of cheese tarts = ³⁰₃₅ of blueberry tarts

Number of more cheese tarts than blueberry tarts at first
= 42 u - 35 u
= 7 u

7 u = 21

1 u = 21 ÷ 7 = 3

Number of cheese tarts that Gem gave away
= 42 u - 30 u
= 12 u
= 12 x 3
= 36

Answer(s): 36