Vanessa and Tom received $312 in total from their father. After Vanessa spent ²₃ of her money and Tom deposited ²₇ of his money into his savings account, Vanessa had thrice as much money as Tom.

1. Find the amount of money Vanessa received from her father.
2. If Tom' savings increased by 25% after the deposit, how much was Tom' savings in the bank in the end?

	Vanessa	Tom	Total
Before	3x15 = 45 u	7 u	$312
Change	- 2x15 = - 30 u	- 2 u
After	1x15 = 15 u	5 u
Comparing Vanessa and Tom in the end	3x5	1x5

Fraction of Vanessa's money left
= 1 - ²₃
= ¹₃

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

The amount that Vanessa had in the end is repeated.  Make the amount that Vanessa had in the end the same. LM of 3 and 1 is 15.

Total amount given to Vanessa and Tom
= 45 u + 7 u
= 52 u

52 u = 312

1 u = 312 ÷ 52 = 6

Amount that Vanessa received from her father
= 45 u
= 45 x 6
= $270

(b)
Amount that Tom deposited
= 2 u
= 2 x 6
= $12

Savings that Tom had at first = 100%

Savings that Tom had in the end
= 100% + 25%
= 125%

25% of the savings = 12
1% of the savings = ¹²₂₅
125% of the savings = 125 x ¹²₂₅ = 60

Tom's savings in the end = $60

Answer(s): (a) $270; (b) $60