Flynn bought 100 brown and gold balloons for a party. The number of gold balloons was ³₇ times as many as the number of brown balloons. Flynn used ¹₃ times as many gold balloons as brown balloons and was left with twice as many gold balloons as brown balloons. How many balloons did Flynn have in the end?

	Gold (1)	Brown (2)	Make b the same. (2)x2 = (3)
Before	30	70	140
Change	- 1 p	- 3 p	- 6 p
After	2 b	1 b	2 b

Number of gold balloons that Flynn bought at first = 3 u
Number of brown balloons that Flynn bought at first = 7 u

Total number of balloons at first
= 3 u + 7 u
= 10 u

10 u = 100

1 u = 100 ÷ 10 = 10

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

Number of brown balloons at first
= 7 u
= 7 x 10
= 70

30 - 1 p = 2 b --- (1)
70 - 3 p = 1 b --- (2)

(2)_x2
140 - 6 p = 2 b --- (3)

(3) = (1)
140 - 6 p = 30 - 1 p
6 p - 1 p = 140 - 30 
5 p = 110

1 p = 110 ÷ 5 = 22

Number of balloons that Flynn used
= 1 p + 3 p
= 4 p
= 4 x 22
= 88

Number of balloons that Flynn had in the end
= 100 - 88
= 12

Answer(s): 12