Eva had a total of 42 pieces of $100 and $50 notes at first. She spent ⁵₈ of the number of $100 notes and received another 2 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 Eva have at first?

	$100	$50	Total
Before	8 u	3 u - 2	42
Change	- 5 u	+ 2
After	3 u
Comparing $100-notes and $50-notes	1x3 = 3 u	1x3 = 3 u

The number of $100-notes and $50-notes in the end is the same.

The number of $100-notes in the end is repeated.  Make the number of $100-notes in the end the same. LCM of 1 and 3 is 3.

Number of notes at first
= 8 u + 3 u - 2
= 11 u - 2

11 u - 2 = 42
11 u = 42 + 2
11 u = 44

1 u = 44 ÷  11 = 4

Number of $100-notes at first
= 8 u
= 8 x 4
= 32

Total value of $100-notes at first
= 32 x 100
= $3200

Number of $50-notes at first
= 3 u - 2
= 3 x 4 - 2
= 12 - 2
= 10

Total value of $50-notes at first
= 10 x 50
= $500

Amount that Eva had at first
= 3200 + 500 
= $3700

Answer(s): $3700