Elyse had a total of 111 pieces of $10 and $20 notes at first. She spent ⁵₈ of the number of $10 notes and received another 10 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 Elyse have at first?

	$10	$20	Total
Before	8 u	3 u - 10	111
Change	- 5 u	+ 10
After	3 u
Comparing $10-notes and $20-notes	1x3 = 3 u	1x3 = 3 u

The number of $10-notes and $20-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 3 is 3.

Number of notes at first
= 8 u + 3 u - 10
= 11 u - 10

11 u - 10 = 111
11 u = 111 + 10
11 u = 121

1 u = 121 ÷  11 = 11

Number of $10-notes at first
= 8 u
= 8 x 11
= 88

Total value of $10-notes at first
= 88 x 10
= $880

Number of $20-notes at first
= 3 u - 10
= 3 x 11 - 10
= 33 - 10
= 23

Total value of $20-notes at first
= 23 x 20
= $460

Amount that Elyse had at first
= 880 + 460 
= $1340

Answer(s): $1340