Natalie had a total of 89 pieces of $5 and $10 notes at first. She spent ³₇ of the number of $5 notes and received another 10 pieces of $10 notes from her mother. After that, the number of $10 notes she had was ¹₂ of the remaining notes. How much money did Natalie have at first?

	$5	$10	Total
Before	7 u	4 u - 10	89
Change	- 3 u	+ 10
After	4 u
Comparing $5-notes and $10-notes	1x4 = 4 u	1x4 = 4 u

The number of $5-notes and $10-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 4 is 4.

Number of notes at first
= 7 u + 4 u - 10
= 11 u - 10

11 u - 10 = 89
11 u = 89 + 10
11 u = 99

1 u = 99 ÷  11 = 9

Number of $5-notes at first
= 7 u
= 7 x 9
= 63

Total value of $5-notes at first
= 63 x 5
= $315

Number of $10-notes at first
= 4 u - 10
= 4 x 9 - 10
= 36 - 10
= 26

Total value of $10-notes at first
= 26 x 10
= $260

Amount that Natalie had at first
= 315 + 260 
= $575

Answer(s): $575