Barbara and Tom received $258 in total from their father. After Barbara spent ⁵₆ of her money and Tom deposited ⁵₇ of his money into his savings account, Barbara had thrice as much money as Tom.

1. Find the amount of money Barbara received from her father.
2. If Tom' savings increased by 30% after the deposit, how much was Tom' savings in the bank in the end?

	Barbara	Tom	Total
Before	6x6 = 36 u	7 u	$258
Change	- 5x6 = - 30 u	- 5 u
After	1x6 = 6 u	2 u
Comparing Barbara and Tom in the end	3x2	1x2

Fraction of Barbara's money left
= 1 - ⁵₆
= ¹₆

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

The amount that Barbara had in the end is repeated.  Make the amount that Barbara had in the end the same. LM of 3 and 1 is 6.

Total amount given to Barbara and Tom
= 36 u + 7 u
= 43 u

43 u = 258

1 u = 258 ÷ 43 = 6

Amount that Barbara received from her father
= 36 u
= 36 x 6
= $216

(b)
Amount that Tom deposited
= 5 u
= 5 x 6
= $30

Savings that Tom had at first = 100%

Savings that Tom had in the end
= 100% + 30%
= 130%

30% of the savings = 30
1% of the savings = ³⁰₃₀
130% of the savings = 130 x ³⁰₃₀ = 130

Tom's savings in the end = $130

Answer(s): (a) $216; (b) $130