Julian had ³₄ as many buttons as Eric. Eric had ⁴₇ as many buttons as Marion. After Julian and Marion gave 8 buttons to Eric, Eric had thrice as many buttons as Julian. Marion then had the same number of buttons as Eric.

1. What was the ratio of the number of buttons Julian had to the number of buttons Marion had in the beginning? Answer in simplest form.
2. How many buttons did Eric have in the end?

Julian	Eric	Marion
3	4
	4	7
3	4	7

(a)
The number of buttons that Eric is repeated.  

Ratio of the number of buttons that Julian had to the number of buttons that Marion had in the beginning = 3 : 7

	Julian	Eric	Marion	Total
Before	3x1 = 3 u	4x1 = 4 u	7x1 = 7 u	14x1 = 14 u
Change	- 8	+ 16	- 8
After	1x2 = 2 u	3x2 = 6 u	3x2 = 6 u	7x2 = 14 u

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

Number of buttons that Eric received from Julian and Marion
= 2 x 8
= 16

Number of buttons that Eric received from Julian and Marion
= 2 x 1 u
= 2 u

2 u = 8

1 u = 8 ÷ 2 = 4

Number of buttons that Ashley had in the end
= 6 u
= 6 x 4
= 24