Abi, Kathy and Lucy shared $540 among themselves. Kathy and Lucy shared ²₉ of the money equally. After Kathy gave away some of her money to Abi, Lucy had 4 times as much money as Kathy. How much money did Kathy give to Abi?

	Kathy	Lucy	Abi	Total
Before	1x4 = 4 u	1x4 = 4 u	7x4 = 28 u	36 u
Change	- 3 u	No change	+ 3 u
After	1x1 = 1 u	4x1 = 4 u	31 u	36 u

Kathy and Lucy shared ²₉ of the money equally.

Fraction of the money that Kathy and Lucy each had
= ²₉ ÷ 2
= ²₉ x ¹₂
= ¹₉

The amount that Lucy had remains unchanged.  The amount that Lucy had is the unchanged quantity. Make the amount that Lucy had the same. LCM of 1 and 4 is 4.

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

Total amount that they had at first
= 4 u + 4 u + 28 u
= 36 u

36 u = 540

1 u = 540 ÷ 36 = 15

Amount that Kathy gave to Abi
= 4 u - 1 u
= 3 u
= 3 x 15
= $45

Answer(s): $45