Joelle had a total of 43 pieces of $10 and $50 notes at first. She spent ³₈ of the number of $10 notes and received another 9 pieces of $50 notes from her mother. After that, the number of $50 notes she had was ¹₂ of the remaining notes. How much money did Joelle have at first?

	$10	$50	Total
Before	8 u	5 u - 9	43
Change	- 3 u	+ 9
After	5 u
Comparing $10-notes and $50-notes	1x5 = 5 u	1x5 = 5 u

The number of $10-notes and $50-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
= 8 u + 5 u - 9
= 13 u - 9

13 u - 9 = 43
13 u = 43 + 9
13 u = 52

1 u = 52 ÷  13 = 4

Number of $10-notes at first
= 8 u
= 8 x 4
= 32

Total value of $10-notes at first
= 32 x 10
= $320

Number of $50-notes at first
= 5 u - 9
= 5 x 4 - 9
= 20 - 9
= 11

Total value of $50-notes at first
= 11 x 50
= $550

Amount that Joelle had at first
= 320 + 550 
= $870

Answer(s): $870