³₅ of Natalie's money was equal to ¹₄ of Barbara's money at first. After Natalie spent $26 and Barbara spent ²₅ of her money, Natalie had ¹₃ as much money as Barbara.

1. How much money did Barbara have at first?
2. How much money did Barbara have in the end?

	Natalie	Barbara
Comparing Natalie and Barbara at first	5x5 = 25 u	12x5 = 60 u
Before		5x12 = 60 u
Change	- $26	- 2x12 = - 24 u
After		3x12 = 36 u
Comparing Natalie  and Barbara in the end	1x12 = 12 u	3x12 = 36 u

³₅ Natalie's money = ¹₄ Barbara's money

Make numerators the same.
35 Natalie's money = 1x34x3 Barbara's money
35 Natalie's money = 312 Barbara's money

Natalie's money : Barbara's money = 5 : 12

The amount that Barbara had at first is repeated.  Make the amount that Barbara had at first the same.  LCM of 12 and 5 is 60.

Amount that Natalie spent
= 25 u - 12 u
= 13 u

13 u = 26

1 u = 26 ÷ 13 = 2

(a)
Amount that Barbara had at first
= 60 u
= 60 x 2
= $120

(b) 
Amount that Barbara had in the end
= 36 u
= 36 x 2
= $72

Answer(s): (a) $120; (b) $72