Emily and Paul received $260 in total from their father. After Emily spent ²₃ of her money and Paul deposited ²₇ of his money into his savings account, Emily had thrice as much money as Paul.

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

	Emily	Paul	Total
Before	3x15 = 45 u	7 u	$260
Change	- 2x15 = - 30 u	- 2 u
After	1x15 = 15 u	5 u
Comparing Emily and Paul in the end	3x5	1x5

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

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

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 15.

Total amount given to Emily and Paul
= 45 u + 7 u
= 52 u

52 u = 260

1 u = 260 ÷ 52 = 5

Amount that Emily received from her father
= 45 u
= 45 x 5
= $225

(b)
Amount that Paul deposited
= 2 u
= 2 x 5
= $10

Savings that Paul had at first = 100%

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

20% of the savings = 10
1% of the savings = ¹⁰₂₀
120% of the savings = 120 x ¹⁰₂₀ = 60

Paul's savings in the end = $60

Answer(s): (a) $225; (b) $60