Nora, Zara and Esther shared $459 among themselves. Zara and Esther shared ²₉ of the money equally. After Zara gave away some of her money to Nora, Esther had 3 times as much money as Zara. How much money did Zara give to Nora?

	Zara	Esther	Nora	Total
Before	1x3 = 3 u	1x3 = 3 u	7x3 = 21 u	27 u
Change	- 2 u	No change	+ 2 u
After	1x1 = 1 u	3x1 = 3 u	23 u	27 u

Zara and Esther shared ²₉ of the money equally.

Fraction of the money that Zara and Esther each had
= ²₉ ÷ 2
= ²₉ x ¹₂
= ¹₉

The amount that Esther had remains unchanged.  The amount that Esther had is the unchanged quantity. Make the amount that Esther had the same. LCM of 1 and 3 is 3.

The amount that Zara and Esther had at first is the same.

Total amount that they had at first
= 3 u + 3 u + 21 u
= 27 u

27 u = 459

1 u = 459 ÷ 27 = 17

Amount that Zara gave to Nora
= 3 u - 1 u
= 2 u
= 2 x 17
= $34

Answer(s): $34