Olivia had a total of 69 pieces of $2 and $5 notes at first. She spent ³₇ of the number of $2 notes and received another 8 pieces of $5 notes from her mother. After that, the number of $5 notes she had was ¹₂ of the remaining notes. How much money did Olivia have at first?

	$2	$5	Total
Before	7 u	4 u - 8	69
Change	- 3 u	+ 8
After	4 u
Comparing $2-notes and $5-notes	1x4 = 4 u	1x4 = 4 u

The number of $2-notes and $5-notes in the end is the same.

The number of $2-notes in the end is repeated.  Make the number of $2-notes in the end the same. LCM of 1 and 4 is 4.

Number of notes at first
= 7 u + 4 u - 8
= 11 u - 8

11 u - 8 = 69
11 u = 69 + 8
11 u = 77

1 u = 77 ÷  11 = 7

Number of $2-notes at first
= 7 u
= 7 x 7
= 49

Total value of $2-notes at first
= 49 x 2
= $98

Number of $5-notes at first
= 4 u - 8
= 4 x 7 - 8
= 28 - 8
= 20

Total value of $5-notes at first
= 20 x 5
= $100

Amount that Olivia had at first
= 98 + 100 
= $198

Answer(s): $198