Fanny, Shannon and Diana shared $546 among themselves. Shannon and Diana shared ³₇ of the money equally. After Shannon gave away some of her money to Fanny, Diana had 3 times as much money as Shannon. How much money did Shannon give to Fanny?

	Shannon	Diana	Fanny	Total
Before	3x3 = 9 u	3x3 = 9 u	8x3 = 24 u	42 u
Change	- 6 u	No change	+ 6 u
After	1x3 = 3 u	3x3 = 9 u	30 u	42 u

Shannon and Diana shared ³₇ of the money equally.

Fraction of the money that Shannon and Diana each had
= ³₇ ÷ 2
= ³₇ x ¹₂
= ³₁₄

The amount that Diana had remains unchanged.  The amount that Diana had is the unchanged quantity. Make the amount that Diana had the same. LCM of 3 and 3 is 9.

The amount that Shannon and Diana had at first is the same.

Total amount that they had at first
= 9 u + 9 u + 24 u
= 42 u

42 u = 546

1 u = 546 ÷ 42 = 13

Amount that Shannon gave to Fanny
= 9 u - 3 u
= 6 u
= 6 x 13
= $78

Answer(s): $78