Penelope had a total of 55 pieces of $20 and $2 notes at first. She spent ³₇ of the number of $20 notes and received another 11 pieces of $2 notes from her mother. After that, the number of $2 notes she had was ¹₂ of the remaining notes. How much money did Penelope have at first?

	$20	$2	Total
Before	7 u	4 u - 11	55
Change	- 3 u	+ 11
After	4 u
Comparing $20-notes and $2-notes	1x4 = 4 u	1x4 = 4 u

The number of $20-notes and $2-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 4 is 4.

Number of notes at first
= 7 u + 4 u - 11
= 11 u - 11

11 u - 11 = 55
11 u = 55 + 11
11 u = 66

1 u = 66 ÷  11 = 6

Number of $20-notes at first
= 7 u
= 7 x 6
= 42

Total value of $20-notes at first
= 42 x 20
= $840

Number of $2-notes at first
= 4 u - 11
= 4 x 6 - 11
= 24 - 11
= 13

Total value of $2-notes at first
= 13 x 2
= $26

Amount that Penelope had at first
= 840 + 26 
= $866

Answer(s): $866