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

	Silver (1)	Blue (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 silver balloons that Glen bought at first = 4 u
Number of blue balloons that Glen 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 silver balloons at first
= 4 u
= 4 x 14
= 56

Number of blue 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 Glen used
= 1 p + 4 p
= 5 p
= 5 x 12
= 60

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

Answer(s): 66