Kimberly had a total of 34 pieces of $20 and $100 notes at first. She spent ⁵₇ of the number of $20 notes and received another 11 pieces of $100 notes from her mother. After that, the number of $100 notes she had was ¹₂ of the remaining notes. How much money did Kimberly have at first?

	$20	$100	Total
Before	7 u	2 u - 11	34
Change	- 5 u	+ 11
After	2 u
Comparing $20-notes and $100-notes	1x2 = 2 u	1x2 = 2 u

The number of $20-notes and $100-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
= 7 u + 2 u - 11
= 9 u - 11

9 u - 11 = 34
9 u = 34 + 11
9 u = 45

1 u = 45 ÷  9 = 5

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

Total value of $20-notes at first
= 35 x 20
= $700

Number of $100-notes at first
= 2 u - 11
= 2 x 5 - 11
= 10 - 11
= -1

Total value of $100-notes at first
= -1 x 100
= $-100

Amount that Kimberly had at first
= 700 + -100 
= $600

Answer(s): $600