Shannon and Natalie had a total of $810 at first. After Shannon spent ³₅ of her money and Natalie spent ¹₂ of her money, they had the same amount of money left.

1. How much money did Shannon have at first?
2. Natalie has the same number of $2-notes and $10-notes at first. How many $10-notes did she have at first?

	Shannon	Natalie	Total
Before	5 u	2x2 = 4 u	9 u
Change	- 3 u	- 1x2 = - 2 u
After	2 u	1x2 = 2 u

(a) 
The amount that Shannon and Natalie had in the end is the same.  Make the amount that they each had in the end the same.  LCM of 1 and 2 is 2. 

Total amount that Shannon and Natalie had at first
= 5 u + 4 u
= 9 u

9 u = 810

1 u = 810 ÷ 9 = 90

Amount that Shannon had at first
= 5 u
= 5 x 90
= $450

(b)
Amount that Natalie had at first
= 4 u
= 4 x 90
= $360

Natalie has the same number of $2-note and $10-note at first.

Value of 1 set of $2-note and $10-note
= 2 + 10
= $12

Number of 2-notes
= 360 ÷ 12
= 30

Answer(s): (a) $450; (b) 30