Xylia had a total of 56 pieces of $10 and $5 notes at first. She spent ⁵₈ of the number of $10 notes and received another 10 pieces of $5 notes from her mother. After that, the number of $5 notes she had was ¹₂ of the remaining notes. How much money did Xylia have at first?

	$10	$5	Total
Before	8 u	3 u - 10	56
Change	- 5 u	+ 10
After	3 u
Comparing $10-notes and $5-notes	1x3 = 3 u	1x3 = 3 u

The number of $10-notes and $5-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 = 56
11 u = 56 + 10
11 u = 66

1 u = 66 ÷  11 = 6

Number of $10-notes at first
= 8 u
= 8 x 6
= 48

Total value of $10-notes at first
= 48 x 10
= $480

Number of $5-notes at first
= 3 u - 10
= 3 x 6 - 10
= 18 - 10
= 8

Total value of $5-notes at first
= 8 x 5
= $40

Amount that Xylia had at first
= 480 + 40 
= $520

Answer(s): $520