Hilda and Liam received $564 in total from their father. After Hilda spent ³₄ of her money and Liam deposited ²₇ of his money into his savings account, Hilda had twice as much money as Liam.

1. Find the amount of money Hilda received from her father.
2. If Liam' savings increased by 40% after the deposit, how much was Liam' savings in the bank in the end?

	Hilda	Liam	Total
Before	4x10 = 40 u	7 u	$564
Change	- 3x10 = - 30 u	- 2 u
After	1x10 = 10 u	5 u
Comparing Hilda and Liam in the end	2x5	1x5

Fraction of Hilda's money left
= 1 - ³₄
= ¹₄

Fraction of Liam's money left
= 1 - ²₇
= ⁵₇

The amount that Hilda had in the end is repeated.  Make the amount that Hilda had in the end the same. LM of 2 and 1 is 10.

Total amount given to Hilda and Liam
= 40 u + 7 u
= 47 u

47 u = 564

1 u = 564 ÷ 47 = 12

Amount that Hilda received from her father
= 40 u
= 40 x 12
= $480

(b)
Amount that Liam deposited
= 2 u
= 2 x 12
= $24

Savings that Liam had at first = 100%

Savings that Liam had in the end
= 100% + 40%
= 140%

40% of the savings = 24
1% of the savings = ²⁴₄₀
140% of the savings = 140 x ²⁴₄₀ = 84

Liam's savings in the end = $84

Answer(s): (a) $480; (b) $84