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

	Grey (1)	White (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 grey balloons that Perry bought at first = 4 u
Number of white balloons that Perry 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 grey balloons at first
= 4 u
= 4 x 14
= 56

Number of white 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 Perry used
= 1 p + 4 p
= 5 p
= 5 x 12
= 60

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

Answer(s): 66