Sean bought 143 grey and brown balloons for a party. The number of brown balloons was ⁴₇ times as many as the number of grey balloons. Sean used ¹₃ times as many brown balloons as grey balloons and was left with twice as many brown balloons as grey balloons. How many balloons did Sean have in the end?

	Brown (1)	Grey (2)	Make b the same. (2)x2 = (3)
Before	52	91	182
Change	- 1 p	- 3 p	- 6 p
After	2 b	1 b	2 b

Number of brown balloons that Sean bought at first = 4 u
Number of grey balloons that Sean bought at first = 7 u

Total number of balloons at first
= 4 u + 7 u
= 11 u

11 u = 143

1 u = 143 ÷ 11 = 13

Number of brown balloons at first
= 4 u
= 4 x 13
= 52

Number of grey balloons at first
= 7 u
= 7 x 13
= 91

52 - 1 p = 2 b --- (1)
91 - 3 p = 1 b --- (2)

(2)_x2
182 - 6 p = 2 b --- (3)

(3) = (1)
182 - 6 p = 52 - 1 p
6 p - 1 p = 182 - 52 
5 p = 130

1 p = 130 ÷ 5 = 26

Number of balloons that Sean used
= 1 p + 3 p
= 4 p
= 4 x 26
= 104

Number of balloons that Sean had in the end
= 143 - 104
= 39

Answer(s): 39