Gem had a total of 114 pieces of $5 and $20 notes at first. She spent ⁵₈ of the number of $5 notes and received another 7 pieces of $20 notes from her mother. After that, the number of $20 notes she had was ¹₂ of the remaining notes. How much money did Gem have at first?

	$5	$20	Total
Before	8 u	3 u - 7	114
Change	- 5 u	+ 7
After	3 u
Comparing $5-notes and $20-notes	1x3 = 3 u	1x3 = 3 u

The number of $5-notes and $20-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 3 is 3.

Number of notes at first
= 8 u + 3 u - 7
= 11 u - 7

11 u - 7 = 114
11 u = 114 + 7
11 u = 121

1 u = 121 ÷  11 = 11

Number of $5-notes at first
= 8 u
= 8 x 11
= 88

Total value of $5-notes at first
= 88 x 5
= $440

Number of $20-notes at first
= 3 u - 7
= 3 x 11 - 7
= 33 - 7
= 26

Total value of $20-notes at first
= 26 x 20
= $520

Amount that Gem had at first
= 440 + 520 
= $960

Answer(s): $960