Esther had a total of 48 pieces of $100 and $2 notes at first. She spent ⁵₈ of the number of $100 notes and received another 7 pieces of $2 notes from her mother. After that, the number of $2 notes she had was ¹₂ of the remaining notes. How much money did Esther have at first?

	$100	$2	Total
Before	8 u	3 u - 7	48
Change	- 5 u	+ 7
After	3 u
Comparing $100-notes and $2-notes	1x3 = 3 u	1x3 = 3 u

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

11 u - 7 = 48
11 u = 48 + 7
11 u = 55

1 u = 55 ÷  11 = 5

Number of $100-notes at first
= 8 u
= 8 x 5
= 40

Total value of $100-notes at first
= 40 x 100
= $4000

Number of $2-notes at first
= 3 u - 7
= 3 x 5 - 7
= 15 - 7
= 8

Total value of $2-notes at first
= 8 x 2
= $16

Amount that Esther had at first
= 4000 + 16 
= $4016

Answer(s): $4016