Vanessa had a total of 37 pieces of $2 and $20 notes at first. She spent ⁵₇ of the number of $2 notes and received another 8 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 Vanessa have at first?

	$2	$20	Total
Before	7 u	2 u - 8	37
Change	- 5 u	+ 8
After	2 u
Comparing $2-notes and $20-notes	1x2 = 2 u	1x2 = 2 u

The number of $2-notes and $20-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 2 is 2.

Number of notes at first
= 7 u + 2 u - 8
= 9 u - 8

9 u - 8 = 37
9 u = 37 + 8
9 u = 45

1 u = 45 ÷  9 = 5

Number of $2-notes at first
= 7 u
= 7 x 5
= 35

Total value of $2-notes at first
= 35 x 2
= $70

Number of $20-notes at first
= 2 u - 8
= 2 x 5 - 8
= 10 - 8
= 2

Total value of $20-notes at first
= 2 x 20
= $40

Amount that Vanessa had at first
= 70 + 40 
= $110

Answer(s): $110