Mary had a total of 79 pieces of $2 and $20 notes at first. She spent ³₈ of the number of $2 notes and received another 12 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 Mary have at first?

	$2	$20	Total
Before	8 u	5 u - 12	79
Change	- 3 u	+ 12
After	5 u
Comparing $2-notes and $20-notes	1x5 = 5 u	1x5 = 5 u

The number of $2-notes and $20-notes in the end is the same.

The number of $2-notes in the end is repeated.  Make the number of $2-notes in the end the same. LCM of 1 and 5 is 5.

Number of notes at first
= 8 u + 5 u - 12
= 13 u - 12

13 u - 12 = 79
13 u = 79 + 12
13 u = 91

1 u = 91 ÷  13 = 7

Number of $2-notes at first
= 8 u
= 8 x 7
= 56

Total value of $2-notes at first
= 56 x 2
= $112

Number of $20-notes at first
= 5 u - 12
= 5 x 7 - 12
= 35 - 12
= 23

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

Amount that Mary had at first
= 112 + 460 
= $572

Answer(s): $572