Elyse had a total of 46 pieces of $100 and $10 notes at first. She spent ³₈ of the number of $100 notes and received another 6 pieces of $10 notes from her mother. After that, the number of $10 notes she had was ¹₂ of the remaining notes. How much money did Elyse have at first?

	$100	$10	Total
Before	8 u	5 u - 6	46
Change	- 3 u	+ 6
After	5 u
Comparing $100-notes and $10-notes	1x5 = 5 u	1x5 = 5 u

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

The number of $100-notes in the end is repeated.  Make the number of $100-notes in the end the same. LCM of 1 and 5 is 5.

Number of notes at first
= 8 u + 5 u - 6
= 13 u - 6

13 u - 6 = 46
13 u = 46 + 6
13 u = 52

1 u = 52 ÷  13 = 4

Number of $100-notes at first
= 8 u
= 8 x 4
= 32

Total value of $100-notes at first
= 32 x 100
= $3200

Number of $10-notes at first
= 5 u - 6
= 5 x 4 - 6
= 20 - 6
= 14

Total value of $10-notes at first
= 14 x 10
= $140

Amount that Elyse had at first
= 3200 + 140 
= $3340

Answer(s): $3340