Min had a total of 42 pieces of $5 and $20 notes at first. She spent ³₈ of the number of $5 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 Min have at first?

	$5	$20	Total
Before	8 u	5 u - 10	42
Change	- 3 u	+ 10
After	5 u
Comparing $5-notes and $20-notes	1x5 = 5 u	1x5 = 5 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 5 is 5.

Number of notes at first
= 8 u + 5 u - 10
= 13 u - 10

13 u - 10 = 42
13 u = 42 + 10
13 u = 52

1 u = 52 ÷  13 = 4

Number of $5-notes at first
= 8 u
= 8 x 4
= 32

Total value of $5-notes at first
= 32 x 5
= $160

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

Total value of $20-notes at first
= 10 x 20
= $200

Amount that Min had at first
= 160 + 200 
= $360

Answer(s): $360