Linda had a total of 53 pieces of $10 and $20 notes at first. She spent ²₅ of the number of $10 notes and received another 3 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 Linda have at first?

	$10	$20	Total
Before	5 u	3 u - 3	53
Change	- 2 u	+ 3
After	3 u
Comparing $10-notes and $20-notes	1x3 = 3 u	1x3 = 3 u

The number of $10-notes and $20-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 3 is 3.

Number of notes at first
= 5 u + 3 u - 3
= 8 u - 3

8 u - 3 = 53
8 u = 53 + 3
8 u = 56

1 u = 56 ÷  8 = 7

Number of $10-notes at first
= 5 u
= 5 x 7
= 35

Total value of $10-notes at first
= 35 x 10
= $350

Number of $20-notes at first
= 3 u - 3
= 3 x 7 - 3
= 21 - 3
= 18

Total value of $20-notes at first
= 18 x 20
= $360

Amount that Linda had at first
= 350 + 360 
= $710

Answer(s): $710