Xuan had a total of 68 pieces of $5 and $20 notes at first. She spent ²₅ of the number of $5 notes and received another 4 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 Xuan have at first?

	$5	$20	Total
Before	5 u	3 u - 4	68
Change	- 2 u	+ 4
After	3 u
Comparing $5-notes and $20-notes	1x3 = 3 u	1x3 = 3 u

The number of $5-notes and $20-notes in the end is the same.

The number of $5-notes in the end is repeated.  Make the number of $5-notes in the end the same. LCM of 1 and 3 is 3.

Number of notes at first
= 5 u + 3 u - 4
= 8 u - 4

8 u - 4 = 68
8 u = 68 + 4
8 u = 72

1 u = 72 ÷  8 = 9

Number of $5-notes at first
= 5 u
= 5 x 9
= 45

Total value of $5-notes at first
= 45 x 5
= $225

Number of $20-notes at first
= 3 u - 4
= 3 x 9 - 4
= 27 - 4
= 23

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

Amount that Xuan had at first
= 225 + 460 
= $685

Answer(s): $685