Michael bought 80 gold and blue balloons for a party. The number of blue balloons was ³₅ times as many as the number of gold balloons. Michael used ¹₄ times as many blue balloons as gold balloons and was left with twice as many blue balloons as gold balloons. How many balloons did Michael have in the end?

	Blue (1)	Gold (2)	Make b the same. (2)x2 = (3)
Before	30	50	100
Change	- 1 p	- 4 p	- 8 p
After	2 b	1 b	2 b

Number of blue balloons that Michael bought at first = 3 u
Number of gold balloons that Michael bought at first = 5 u

Total number of balloons at first
= 3 u + 5 u
= 8 u

8 u = 80

1 u = 80 ÷ 8 = 10

Number of blue balloons at first
= 3 u
= 3 x 10
= 30

Number of gold balloons at first
= 5 u
= 5 x 10
= 50

30 - 1 p = 2 b --- (1)
50 - 4 p = 1 b --- (2)

(2)_x2
100 - 8 p = 2 b --- (3)

(3) = (1)
100 - 8 p = 30 - 1 p
8 p - 1 p = 100 - 30 
7 p = 70

1 p = 70 ÷ 7 = 10

Number of balloons that Michael used
= 1 p + 4 p
= 5 p
= 5 x 10
= 50

Number of balloons that Michael had in the end
= 80 - 50
= 30

Answer(s): 30