Hazel and Rachel have some tarts each. If Hazel gives Rachel 20 tarts, Hazel will have ³₄ as many tarts as Rachel. If Hazel gives Rachel 11 tarts, they will have an equal number of tarts. How many tarts does Hazel have at first?

	Case 1		Case 2
	Hazel	Rachel	Hazel	Rachel
Before	3 u + 20	4 u - 20	3.5 u + 11	3.5 u - 11
Change	- 20	+ 20	- 11	+ 11
After	3 u	4 u	3.5 u	3.5 u

Total number of tarts that Hazel and Rachel have
= 3 u + 4 u
= 7 u 

Number of tarts that Hazel and Rachel each has in the end is the same.

Number of tarts that Hazel and Rachel each has in the end in Case 2
= 7 u ÷ 2
= 3.5 u

Number of tarts that Hazel had at first is the same in Case 1 and Case 2.

3.5 u + 11 = 3 u + 20
3.5 u - 3 u = 20 - 11
0.5 u = 9

1 u = 9 ÷ 0.5 = 18

Number of tarts that Hazel has
= 3 u + 20
= 3 x 18 + 20
= 54 + 20
= 74

Answer(s): 74