Emma, Yen and Gem shared $216 among themselves. Yen and Gem shared ²₉ of the money equally. After Yen gave away some of her money to Emma, Gem had 6 times as much money as Yen. How much money did Yen give to Emma?

	Yen	Gem	Emma	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

Yen and Gem shared ²₉ of the money equally.

Fraction of the money that Yen and Gem each had
= ²₉ ÷ 2
= ²₉ x ¹₂
= ¹₉

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

The amount that Yen and Gem had at first is the same.

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

54 u = 216

1 u = 216 ÷ 54 = 4

Amount that Yen gave to Emma
= 6 u - 1 u
= 5 u
= 5 x 4
= $20

Answer(s): $20