Victoria had a total of 83 pieces of $10 and $5 notes at first. She spent ⁵₇ of the number of $10 notes and received another 7 pieces of $5 notes from her mother. After that, the number of $5 notes she had was ¹₂ of the remaining notes. How much money did Victoria have at first?

	$10	$5	Total
Before	7 u	2 u - 7	83
Change	- 5 u	+ 7
After	2 u
Comparing $10-notes and $5-notes	1x2 = 2 u	1x2 = 2 u

The number of $10-notes and $5-notes in the end is the same.

The number of $10-notes in the end is repeated.  Make the number of $10-notes in the end the same. LCM of 1 and 2 is 2.

Number of notes at first
= 7 u + 2 u - 7
= 9 u - 7

9 u - 7 = 83
9 u = 83 + 7
9 u = 90

1 u = 90 ÷  9 = 10

Number of $10-notes at first
= 7 u
= 7 x 10
= 70

Total value of $10-notes at first
= 70 x 10
= $700

Number of $5-notes at first
= 2 u - 7
= 2 x 10 - 7
= 20 - 7
= 13

Total value of $5-notes at first
= 13 x 5
= $65

Amount that Victoria had at first
= 700 + 65 
= $765

Answer(s): $765