Olivia had a total of 33 pieces of $5 and $20 notes at first. She spent ³₅ of the number of $5 notes and received another 9 pieces of $20 notes from her mother. After that, the number of $20 notes she had was ¹₂ of the remaining notes. How much money did Olivia have at first?

	$5	$20	Total
Before	5 u	2 u - 9	33
Change	- 3 u	+ 9
After	2 u
Comparing $5-notes and $20-notes	1x2 = 2 u	1x2 = 2 u

The number of $5-notes and $20-notes in the end is the same.

The number of $5-notes in the end is repeated.  Make the number of $5-notes in the end the same. LCM of 1 and 2 is 2.

Number of notes at first
= 5 u + 2 u - 9
= 7 u - 9

7 u - 9 = 33
7 u = 33 + 9
7 u = 42

1 u = 42 ÷  7 = 6

Number of $5-notes at first
= 5 u
= 5 x 6
= 30

Total value of $5-notes at first
= 30 x 5
= $150

Number of $20-notes at first
= 2 u - 9
= 2 x 6 - 9
= 12 - 9
= 3

Total value of $20-notes at first
= 3 x 20
= $60

Amount that Olivia had at first
= 150 + 60 
= $210

Answer(s): $210