Zoe had a total of 89 pieces of $10 and $2 notes at first. She spent ²₇ of the number of $10 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 Zoe have at first?

	$10	$2	Total
Before	7 u	5 u - 7	89
Change	- 2 u	+ 7
After	5 u
Comparing $10-notes and $2-notes	1x5 = 5 u	1x5 = 5 u

The number of $10-notes and $2-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 5 is 5.

Number of notes at first
= 7 u + 5 u - 7
= 12 u - 7

12 u - 7 = 89
12 u = 89 + 7
12 u = 96

1 u = 96 ÷  12 = 8

Number of $10-notes at first
= 7 u
= 7 x 8
= 56

Total value of $10-notes at first
= 56 x 10
= $560

Number of $2-notes at first
= 5 u - 7
= 5 x 8 - 7
= 40 - 7
= 33

Total value of $2-notes at first
= 33 x 2
= $66

Amount that Zoe had at first
= 560 + 66 
= $626

Answer(s): $626