Opal had a total of 11 pieces of $20 and $5 notes at first. She spent ³₅ of the number of $20 notes and received another 3 pieces of $5 notes from her mother. After that, the number of $5 notes she had was ¹₂ of the remaining notes. How much money did Opal have at first?

	$20	$5	Total
Before	5 u	2 u - 3	11
Change	- 3 u	+ 3
After	2 u
Comparing $20-notes and $5-notes	1x2 = 2 u	1x2 = 2 u

The number of $20-notes and $5-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 - 3
= 7 u - 3

7 u - 3 = 11
7 u = 11 + 3
7 u = 14

1 u = 14 ÷  7 = 2

Number of $20-notes at first
= 5 u
= 5 x 2
= 10

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

Number of $5-notes at first
= 2 u - 3
= 2 x 2 - 3
= 4 - 3
= 1

Total value of $5-notes at first
= 1 x 5
= $5

Amount that Opal had at first
= 200 + 5 
= $205

Answer(s): $205