Sean had ³₄ as many buttons as Andy. Andy had ⁴₇ as many buttons as Linda. After Sean and Linda gave 10 buttons to Andy, Andy had thrice as many buttons as Sean. Linda then had the same number of buttons as Andy.

1. What was the ratio of the number of buttons Sean had to the number of buttons Linda had in the beginning? Answer in simplest form.
2. How many buttons did Andy have in the end?

Sean	Andy	Linda
3	4
	4	7
3	4	7

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

Ratio of the number of buttons that Sean had to the number of buttons that Linda had in the beginning = 3 : 7

	Sean	Andy	Linda	Total
Before	3x1 = 3 u	4x1 = 4 u	7x1 = 7 u	14x1 = 14 u
Change	- 10	+ 20	- 10
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 Andy received from Sean and Linda
= 2 x 10
= 20

Number of buttons that Andy received from Sean and Linda
= 2 x 1 u
= 2 u

2 u = 10

1 u = 10 ÷ 2 = 5

Number of buttons that Ashley had in the end
= 6 u
= 6 x 5
= 30