Kathy, Jen and Kimberly shared $270 among themselves. Jen and Kimberly shared ⁴₉ of the money equally. After Jen gave away some of her money to Kathy, Kimberly had 6 times as much money as Jen. How much money did Jen give to Kathy?

	Jen	Kimberly	Kathy	Total
Before	2x6 = 12 u	2x6 = 12 u	5x6 = 30 u	54 u
Change	- 10 u	No change	+ 10 u
After	1x2 = 2 u	6x2 = 12 u	40 u	54 u

Jen and Kimberly shared ⁴₉ of the money equally.

Fraction of the money that Jen and Kimberly each had
= ⁴₉ ÷ 2
= ⁴₉ x ¹₂
= ²₉

The amount that Kimberly had remains unchanged.  The amount that Kimberly had is the unchanged quantity. Make the amount that Kimberly had the same. LCM of 2 and 6 is 12.

The amount that Jen and Kimberly had at first is the same.

Total amount that they had at first
= 12 u + 12 u + 30 u
= 54 u

54 u = 270

1 u = 270 ÷ 54 = 5

Amount that Jen gave to Kathy
= 12 u - 2 u
= 10 u
= 10 x 5
= $50

Answer(s): $50