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

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

Bobby	Julian	Erika
3	4
	4	7
3	4	7

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

Ratio of the number of buttons that Erika had to the number of buttons that Bobby had in the beginning = 7 : 3

	Bobby	Julian	Erika	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 Julian received from Bobby and Erika
= 2 x 8
= 16

Number of buttons that Julian received from Bobby and Erika
= 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