Lucy, Zara and Sabrina shared $585 among themselves. Zara and Sabrina shared ²₉ of the money equally. After Zara gave away some of her money to Lucy, Sabrina had 5 times as much money as Zara. How much money did Zara give to Lucy?

	Zara	Sabrina	Lucy	Total
Before	1x5 = 5 u	1x5 = 5 u	7x5 = 35 u	45 u
Change	- 4 u	No change	+ 4 u
After	1x1 = 1 u	5x1 = 5 u	39 u	45 u

Zara and Sabrina shared ²₉ of the money equally.

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

The amount that Sabrina had remains unchanged.  The amount that Sabrina had is the unchanged quantity. Make the amount that Sabrina had the same. LCM of 1 and 5 is 5.

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

Total amount that they had at first
= 5 u + 5 u + 35 u
= 45 u

45 u = 585

1 u = 585 ÷ 45 = 13

Amount that Zara gave to Lucy
= 5 u - 1 u
= 4 u
= 4 x 13
= $52

Answer(s): $52