Vanessa had a total of 154 pieces of $10 and $100 notes at first. She spent ³₈ of the number of $10 notes and received another 2 pieces of $100 notes from her mother. After that, the number of $100 notes she had was ¹₂ of the remaining notes. How much money did Vanessa have at first?

	$10	$100	Total
Before	8 u	5 u - 2	154
Change	- 3 u	+ 2
After	5 u
Comparing $10-notes and $100-notes	1x5 = 5 u	1x5 = 5 u

The number of $10-notes and $100-notes in the end is the same.

The number of $10-notes in the end is repeated.  Make the number of $10-notes in the end the same. LCM of 1 and 5 is 5.

Number of notes at first
= 8 u + 5 u - 2
= 13 u - 2

13 u - 2 = 154
13 u = 154 + 2
13 u = 156

1 u = 156 ÷  13 = 12

Number of $10-notes at first
= 8 u
= 8 x 12
= 96

Total value of $10-notes at first
= 96 x 10
= $960

Number of $100-notes at first
= 5 u - 2
= 5 x 12 - 2
= 60 - 2
= 58

Total value of $100-notes at first
= 58 x 100
= $5800

Amount that Vanessa had at first
= 960 + 5800 
= $6760

Answer(s): $6760