Eric had ³₄ as many coins as Luis. Luis had ⁴₇ as many coins as Jade. After Eric and Jade gave 12 coins to Luis, Luis had thrice as many coins as Eric. Jade then had the same number of coins as Luis.

1. What was the ratio of the number of coins Jade had to the number of coins Eric had in the beginning? Answer in simplest form.
2. How many coins did Luis have in the end?

Eric	Luis	Jade
3	4
	4	7
3	4	7

(a)
The number of coins that Luis is repeated.  

Ratio of the number of coins that Jade had to the number of coins that Eric had in the beginning = 7 : 3

	Eric	Luis	Jade	Total
Before	3x1 = 3 u	4x1 = 4 u	7x1 = 7 u	14x1 = 14 u
Change	- 12	+ 24	- 12
After	1x2 = 2 u	3x2 = 6 u	3x2 = 6 u	7x2 = 14 u

The total number of coins at first and in the end remains unchanged. Make the total number of coins the same. LCM of 14 and 7 is 14.

Number of coins that Luis received from Eric and Jade
= 2 x 12
= 24

Number of coins that Luis received from Eric and Jade
= 2 x 1 u
= 2 u

2 u = 12

1 u = 12 ÷ 2 = 6

Number of coins that Ashley had in the end
= 6 u
= 6 x 6
= 36