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

	Pink (1)	Black (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 pink balloons that Henry bought at first = 4 u
Number of black balloons that Henry 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 pink balloons at first
= 4 u
= 4 x 14
= 56

Number of black 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 Henry used
= 1 p + 4 p
= 5 p
= 5 x 12
= 60

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

Answer(s): 66