Elyse and Rachel have some tarts each. If Elyse gives Rachel 14 tarts, Elyse will have ²₉ as many tarts as Rachel. If Elyse gives Rachel 7 tarts, they will have an equal number of tarts. How many tarts does Elyse have at first?

	Case 1		Case 2
	Elyse	Rachel	Elyse	Rachel
Before	2 u + 14	9 u - 14	5.5 u + 7	5.5 u - 7
Change	- 14	+ 14	- 7	+ 7
After	2 u	9 u	5.5 u	5.5 u

Total number of tarts that Elyse and Rachel have
= 2 u + 9 u
= 11 u 

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

Number of tarts that Elyse and Rachel each has in the end in Case 2
= 11 u ÷ 2
= 5.5 u

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

5.5 u + 7 = 2 u + 14
5.5 u - 2 u = 14 - 7
0.5 u = 7

1 u = 7 ÷ 0.5 = 14

Number of tarts that Elyse has
= 2 u + 14
= 2 x 14 + 14
= 28 + 14
= 42

Answer(s): 42