Nora had a total of 51 pieces of $20 and $50 notes at first. She spent ³₅ of the number of $20 notes and received another 5 pieces of $50 notes from her mother. After that, the number of $50 notes she had was ¹₂ of the remaining notes. How much money did Nora have at first?

	$20	$50	Total
Before	5 u	2 u - 5	51
Change	- 3 u	+ 5
After	2 u
Comparing $20-notes and $50-notes	1x2 = 2 u	1x2 = 2 u

The number of $20-notes and $50-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 2 is 2.

Number of notes at first
= 5 u + 2 u - 5
= 7 u - 5

7 u - 5 = 51
7 u = 51 + 5
7 u = 56

1 u = 56 ÷  7 = 8

Number of $20-notes at first
= 5 u
= 5 x 8
= 40

Total value of $20-notes at first
= 40 x 20
= $800

Number of $50-notes at first
= 2 u - 5
= 2 x 8 - 5
= 16 - 5
= 11

Total value of $50-notes at first
= 11 x 50
= $550

Amount that Nora had at first
= 800 + 550 
= $1350

Answer(s): $1350