Roshel, Rachel and Lucy shared $459 among themselves. Rachel and Lucy shared ⁴₉ of the money equally. After Rachel gave away some of her money to Roshel, Lucy had 3 times as much money as Rachel. How much money did Rachel give to Roshel?

	Rachel	Lucy	Roshel	Total
Before	2x3 = 6 u	2x3 = 6 u	5x3 = 15 u	27 u
Change	- 4 u	No change	+ 4 u
After	1x2 = 2 u	3x2 = 6 u	19 u	27 u

Rachel and Lucy shared ⁴₉ of the money equally.

Fraction of the money that Rachel and Lucy each had
= ⁴₉ ÷ 2
= ⁴₉ x ¹₂
= ²₉

The amount that Lucy had remains unchanged.  The amount that Lucy had is the unchanged quantity. Make the amount that Lucy had the same. LCM of 2 and 3 is 6.

The amount that Rachel and Lucy had at first is the same.

Total amount that they had at first
= 6 u + 6 u + 15 u
= 27 u

27 u = 459

1 u = 459 ÷ 27 = 17

Amount that Rachel gave to Roshel
= 6 u - 2 u
= 4 u
= 4 x 17
= $68

Answer(s): $68