Kathy and Luis received $184 in total from their father. After Kathy spent ³₄ of her money and Luis deposited ⁵₇ of his money into his savings account, Kathy had twice as much money as Luis.

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

	Kathy	Luis	Total
Before	4x4 = 16 u	7 u	$184
Change	- 3x4 = - 12 u	- 5 u
After	1x4 = 4 u	2 u
Comparing Kathy and Luis in the end	2x2	1x2

Fraction of Kathy's money left
= 1 - ³₄
= ¹₄

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

The amount that Kathy had in the end is repeated.  Make the amount that Kathy had in the end the same. LM of 2 and 1 is 4.

Total amount given to Kathy and Luis
= 16 u + 7 u
= 23 u

23 u = 184

1 u = 184 ÷ 23 = 8

Amount that Kathy received from her father
= 16 u
= 16 x 8
= $128

(b)
Amount that Luis deposited
= 5 u
= 5 x 8
= $40

Savings that Luis had at first = 100%

Savings that Luis 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

Luis's savings in the end = $240

Answer(s): (a) $128; (b) $240