Dana, Lucy and Jane shared $224 among themselves. Lucy and Jane shared ³₇ of the money equally. After Lucy gave away some of her money to Dana, Jane had 4 times as much money as Lucy. How much money did Lucy give to Dana?

	Lucy	Jane	Dana	Total
Before	3x4 = 12 u	3x4 = 12 u	8x4 = 32 u	56 u
Change	- 9 u	No change	+ 9 u
After	1x3 = 3 u	4x3 = 12 u	41 u	56 u

Lucy and Jane shared ³₇ of the money equally.

Fraction of the money that Lucy and Jane each had
= ³₇ ÷ 2
= ³₇ x ¹₂
= ³₁₄

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

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

Total amount that they had at first
= 12 u + 12 u + 32 u
= 56 u

56 u = 224

1 u = 224 ÷ 56 = 4

Amount that Lucy gave to Dana
= 12 u - 3 u
= 9 u
= 9 x 4
= $36

Answer(s): $36