Lucy had a total of 42 pieces of $10 and $20 notes at first. She spent ³₅ of the number of $10 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 Lucy have at first?

	$10	$20	Total
Before	5 u	2 u - 7	42
Change	- 3 u	+ 7
After	2 u
Comparing $10-notes and $20-notes	1x2 = 2 u	1x2 = 2 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 2 is 2.

Number of notes at first
= 5 u + 2 u - 7
= 7 u - 7

7 u - 7 = 42
7 u = 42 + 7
7 u = 49

1 u = 49 ÷  7 = 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
= 2 u - 7
= 2 x 7 - 7
= 14 - 7
= 7

Total value of $20-notes at first
= 7 x 20
= $140

Amount that Lucy had at first
= 350 + 140 
= $490

Answer(s): $490