Hilda had a total of 41 pieces of $20 and $50 notes at first. She spent ⁵₈ of the number of $20 notes and received another 3 pieces of $50 notes from her mother. After that, the number of $50 notes she had was ¹₂ of the remaining notes. How much money did Hilda have at first?

	$20	$50	Total
Before	8 u	3 u - 3	41
Change	- 5 u	+ 3
After	3 u
Comparing $20-notes and $50-notes	1x3 = 3 u	1x3 = 3 u

The number of $20-notes and $50-notes in the end is the same.

The number of $20-notes in the end is repeated.  Make the number of $20-notes in the end the same. LCM of 1 and 3 is 3.

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

11 u - 3 = 41
11 u = 41 + 3
11 u = 44

1 u = 44 ÷  11 = 4

Number of $20-notes at first
= 8 u
= 8 x 4
= 32

Total value of $20-notes at first
= 32 x 20
= $640

Number of $50-notes at first
= 3 u - 3
= 3 x 4 - 3
= 12 - 3
= 9

Total value of $50-notes at first
= 9 x 50
= $450

Amount that Hilda had at first
= 640 + 450 
= $1090

Answer(s): $1090