Tiffany had a total of 83 pieces of $50 and $100 notes at first. She spent ²₅ of the number of $50 notes and received another 5 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 Tiffany have at first?

	$50	$100	Total
Before	5 u	3 u - 5	83
Change	- 2 u	+ 5
After	3 u
Comparing $50-notes and $100-notes	1x3 = 3 u	1x3 = 3 u

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

The number of $50-notes in the end is repeated.  Make the number of $50-notes in the end the same. LCM of 1 and 3 is 3.

Number of notes at first
= 5 u + 3 u - 5
= 8 u - 5

8 u - 5 = 83
8 u = 83 + 5
8 u = 88

1 u = 88 ÷  8 = 11

Number of $50-notes at first
= 5 u
= 5 x 11
= 55

Total value of $50-notes at first
= 55 x 50
= $2750

Number of $100-notes at first
= 3 u - 5
= 3 x 11 - 5
= 33 - 5
= 28

Total value of $100-notes at first
= 28 x 100
= $2800

Amount that Tiffany had at first
= 2750 + 2800 
= $5550

Answer(s): $5550