Kylie, Penelope and Zoe shared $546 among themselves. Penelope and Zoe shared ²₇ of the money equally. After Penelope gave away some of her money to Kylie, Zoe had 3 times as much money as Penelope. How much money did Penelope give to Kylie?

	Penelope	Zoe	Kylie	Total
Before	1x3 = 3 u	1x3 = 3 u	5x3 = 15 u	21 u
Change	- 2 u	No change	+ 2 u
After	1x1 = 1 u	3x1 = 3 u	17 u	21 u

Penelope and Zoe shared ²₇ of the money equally.

Fraction of the money that Penelope and Zoe each had
= ²₇ ÷ 2
= ²₇ x ¹₂
= ¹₇

The amount that Zoe had remains unchanged.  The amount that Zoe had is the unchanged quantity. Make the amount that Zoe had the same. LCM of 1 and 3 is 3.

The amount that Penelope and Zoe had at first is the same.

Total amount that they had at first
= 3 u + 3 u + 15 u
= 21 u

21 u = 546

1 u = 546 ÷ 21 = 26

Amount that Penelope gave to Kylie
= 3 u - 1 u
= 2 u
= 2 x 26
= $52

Answer(s): $52