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

	Black (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 black balloons that Michael bought at first = 4 u
Number of grey balloons that Michael 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 black 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 Michael used
= 1 p + 3 p
= 4 p
= 4 x 26
= 104

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

Answer(s): 39