Esther had a total of 45 pieces of $5 and $2 notes at first. She spent ³₅ of the number of $5 notes and received another 4 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?

	$5	$2	Total
Before	5 u	2 u - 4	45
Change	- 3 u	+ 4
After	2 u
Comparing $5-notes and $2-notes	1x2 = 2 u	1x2 = 2 u

The number of $5-notes and $2-notes in the end is the same.

The number of $5-notes in the end is repeated.  Make the number of $5-notes in the end the same. LCM of 1 and 2 is 2.

Number of notes at first
= 5 u + 2 u - 4
= 7 u - 4

7 u - 4 = 45
7 u = 45 + 4
7 u = 49

1 u = 49 ÷  7 = 7

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

Total value of $5-notes at first
= 35 x 5
= $175

Number of $2-notes at first
= 2 u - 4
= 2 x 7 - 4
= 14 - 4
= 10

Total value of $2-notes at first
= 10 x 2
= $20

Amount that Esther had at first
= 175 + 20 
= $195

Answer(s): $195