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

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

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

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

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

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

Total amount given to Emily and Rael
= 36 u + 7 u
= 43 u

43 u = 258

1 u = 258 ÷ 43 = 6

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

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

Savings that Rael had at first = 100%

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

25% of the savings = 30
1% of the savings = ³⁰₂₅
125% of the savings = 125 x ³⁰₂₅ = 150

Rael's savings in the end = $150

Answer(s): (a) $216; (b) $150