Penelope and Zane received $670 in total from their father. After Penelope spent ⁴₅ of her money and Zane deposited ⁴₇ of his money into his savings account, Penelope had four times as much money as Zane.

1. Find the amount of money Penelope received from her father.
2. If Zane' savings increased by 20% after the deposit, how much was Zane' savings in the bank in the end?

	Penelope	Zane	Total
Before	5x12 = 60 u	7 u	$670
Change	- 4x12 = - 48 u	- 4 u
After	1x12 = 12 u	3 u
Comparing Penelope and Zane in the end	4x3	1x3

Fraction of Penelope's money left
= 1 - ⁴₅
= ¹₅

Fraction of Zane's money left
= 1 - ⁴₇
= ³₇

The amount that Penelope had in the end is repeated.  Make the amount that Penelope had in the end the same. LM of 4 and 1 is 12.

Total amount given to Penelope and Zane
= 60 u + 7 u
= 67 u

67 u = 670

1 u = 670 ÷ 67 = 10

Amount that Penelope received from her father
= 60 u
= 60 x 10
= $600

(b)
Amount that Zane deposited
= 4 u
= 4 x 10
= $40

Savings that Zane had at first = 100%

Savings that Zane had in the end
= 100% + 20%
= 120%

20% of the savings = 40
1% of the savings = ⁴⁰₂₀
120% of the savings = 120 x ⁴⁰₂₀ = 240

Zane's savings in the end = $240

Answer(s): (a) $600; (b) $240