Shannon, Vanessa and Joelle shared $462 among themselves. Vanessa and Joelle shared ²₇ of the money equally. After Vanessa gave away some of her money to Shannon, Joelle had 6 times as much money as Vanessa. How much money did Vanessa give to Shannon?

	Vanessa	Joelle	Shannon	Total
Before	1x6 = 6 u	1x6 = 6 u	5x6 = 30 u	42 u
Change	- 5 u	No change	+ 5 u
After	1x1 = 1 u	6x1 = 6 u	35 u	42 u

Vanessa and Joelle shared ²₇ of the money equally.

Fraction of the money that Vanessa and Joelle each had
= ²₇ ÷ 2
= ²₇ x ¹₂
= ¹₇

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

The amount that Vanessa and Joelle had at first is the same.

Total amount that they had at first
= 6 u + 6 u + 30 u
= 42 u

42 u = 462

1 u = 462 ÷ 42 = 11

Amount that Vanessa gave to Shannon
= 6 u - 1 u
= 5 u
= 5 x 11
= $55

Answer(s): $55