Barbara had a total of 142 pieces of $20 and $100 notes at first. She spent ²₇ of the number of $20 notes and received another 2 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 Barbara have at first?

	$20	$100	Total
Before	7 u	5 u - 2	142
Change	- 2 u	+ 2
After	5 u
Comparing $20-notes and $100-notes	1x5 = 5 u	1x5 = 5 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 5 is 5.

Number of notes at first
= 7 u + 5 u - 2
= 12 u - 2

12 u - 2 = 142
12 u = 142 + 2
12 u = 144

1 u = 144 ÷  12 = 12

Number of $20-notes at first
= 7 u
= 7 x 12
= 84

Total value of $20-notes at first
= 84 x 20
= $1680

Number of $100-notes at first
= 5 u - 2
= 5 x 12 - 2
= 60 - 2
= 58

Total value of $100-notes at first
= 58 x 100
= $5800

Amount that Barbara had at first
= 1680 + 5800 
= $7480

Answer(s): $7480