Fabian bought 126 purple and green balloons for a party. The number of green balloons was ⁴₅ times as many as the number of purple balloons. Fabian used ¹₄ times as many green balloons as purple balloons and was left with twice as many green balloons as purple balloons. How many balloons did Fabian have in the end?

	Green (1)	Purple (2)	Make b the same. (2)x2 = (3)
Before	56	70	140
Change	- 1 p	- 4 p	- 8 p
After	2 b	1 b	2 b

Number of green balloons that Fabian bought at first = 4 u
Number of purple balloons that Fabian bought at first = 5 u

Total number of balloons at first
= 4 u + 5 u
= 9 u

9 u = 126

1 u = 126 ÷ 9 = 14

Number of green balloons at first
= 4 u
= 4 x 14
= 56

Number of purple balloons at first
= 5 u
= 5 x 14
= 70

56 - 1 p = 2 b --- (1)
70 - 4 p = 1 b --- (2)

(2)_x2
140 - 8 p = 2 b --- (3)

(3) = (1)
140 - 8 p = 56 - 1 p
8 p - 1 p = 140 - 56 
7 p = 84

1 p = 84 ÷ 7 = 12

Number of balloons that Fabian used
= 1 p + 4 p
= 5 p
= 5 x 12
= 60

Number of balloons that Fabian had in the end
= 126 - 60
= 66

Answer(s): 66