Penelope, Gwen and Hazel shared $320 among themselves. Gwen and Hazel shared ³₈ of the money equally. After Gwen gave away some of her money to Penelope, Hazel had 4 times as much money as Gwen. How much money did Gwen give to Penelope?

	Gwen	Hazel	Penelope	Total
Before	3x4 = 12 u	3x4 = 12 u	10x4 = 40 u	64 u
Change	- 9 u	No change	+ 9 u
After	1x3 = 3 u	4x3 = 12 u	49 u	64 u

Gwen and Hazel shared ³₈ of the money equally.

Fraction of the money that Gwen and Hazel each had
= ³₈ ÷ 2
= ³₈ x ¹₂
= ³₁₆

The amount that Hazel had remains unchanged.  The amount that Hazel had is the unchanged quantity. Make the amount that Hazel had the same. LCM of 3 and 4 is 12.

The amount that Gwen and Hazel had at first is the same.

Total amount that they had at first
= 12 u + 12 u + 40 u
= 64 u

64 u = 320

1 u = 320 ÷ 64 = 5

Amount that Gwen gave to Penelope
= 12 u - 3 u
= 9 u
= 9 x 5
= $45

Answer(s): $45