Diana, Roshel and Opal shared $540 among themselves. Roshel and Opal shared ²₉ of the money equally. After Roshel gave away some of her money to Diana, Opal had 6 times as much money as Roshel. How much money did Roshel give to Diana?

	Roshel	Opal	Diana	Total
Before	1x6 = 6 u	1x6 = 6 u	7x6 = 42 u	54 u
Change	- 5 u	No change	+ 5 u
After	1x1 = 1 u	6x1 = 6 u	47 u	54 u

Roshel and Opal shared ²₉ of the money equally.

Fraction of the money that Roshel and Opal each had
= ²₉ ÷ 2
= ²₉ x ¹₂
= ¹₉

The amount that Opal had remains unchanged.  The amount that Opal had is the unchanged quantity. Make the amount that Opal had the same. LCM of 1 and 6 is 6.

The amount that Roshel and Opal had at first is the same.

Total amount that they had at first
= 6 u + 6 u + 42 u
= 54 u

54 u = 540

1 u = 540 ÷ 54 = 10

Amount that Roshel gave to Diana
= 6 u - 1 u
= 5 u
= 5 x 10
= $50

Answer(s): $50