Emily had a total of 97 pieces of $50 and $5 notes at first. She spent ⁵₇ of the number of $50 notes and received another 11 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 Emily have at first?

	$50	$5	Total
Before	7 u	2 u - 11	97
Change	- 5 u	+ 11
After	2 u
Comparing $50-notes and $5-notes	1x2 = 2 u	1x2 = 2 u

The number of $50-notes and $5-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 2 is 2.

Number of notes at first
= 7 u + 2 u - 11
= 9 u - 11

9 u - 11 = 97
9 u = 97 + 11
9 u = 108

1 u = 108 ÷  9 = 12

Number of $50-notes at first
= 7 u
= 7 x 12
= 84

Total value of $50-notes at first
= 84 x 50
= $4200

Number of $5-notes at first
= 2 u - 11
= 2 x 12 - 11
= 24 - 11
= 13

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

Amount that Emily had at first
= 4200 + 65 
= $4265

Answer(s): $4265