Gillian had a total of 10 pieces of $50 and $100 notes at first. She spent ⁴₇ of the number of $50 notes and received another 10 pieces of $100 notes from her mother. After that, the number of $100 notes she had was ¹₂ of the remaining notes. How much money did Gillian have at first?

	$50	$100	Total
Before	7 u	3 u - 10	10
Change	- 4 u	+ 10
After	3 u
Comparing $50-notes and $100-notes	1x3 = 3 u	1x3 = 3 u

The number of $50-notes and $100-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 3 is 3.

Number of notes at first
= 7 u + 3 u - 10
= 10 u - 10

10 u - 10 = 10
10 u = 10 + 10
10 u = 20

1 u = 20 ÷  10 = 2

Number of $50-notes at first
= 7 u
= 7 x 2
= 14

Total value of $50-notes at first
= 14 x 50
= $700

Number of $100-notes at first
= 3 u - 10
= 3 x 2 - 10
= 6 - 10
= -4

Total value of $100-notes at first
= -4 x 100
= $-400

Amount that Gillian had at first
= 700 + -400 
= $300

Answer(s): $300