Julian bought 220 pink and gold balloons for a party. The number of gold balloons was ⁴₇ times as many as the number of pink balloons. Julian used ¹₃ times as many gold balloons as pink balloons and was left with twice as many gold balloons as pink balloons. How many balloons did Julian have in the end?

	Gold (1)	Pink (2)	Make b the same. (2)x2 = (3)
Before	80	140	280
Change	- 1 p	- 3 p	- 6 p
After	2 b	1 b	2 b

Number of gold balloons that Julian bought at first = 4 u
Number of pink balloons that Julian bought at first = 7 u

Total number of balloons at first
= 4 u + 7 u
= 11 u

11 u = 220

1 u = 220 ÷ 11 = 20

Number of gold balloons at first
= 4 u
= 4 x 20
= 80

Number of pink balloons at first
= 7 u
= 7 x 20
= 140

80 - 1 p = 2 b --- (1)
140 - 3 p = 1 b --- (2)

(2)_x2
280 - 6 p = 2 b --- (3)

(3) = (1)
280 - 6 p = 80 - 1 p
6 p - 1 p = 280 - 80 
5 p = 200

1 p = 200 ÷ 5 = 40

Number of balloons that Julian used
= 1 p + 3 p
= 4 p
= 4 x 40
= 160

Number of balloons that Julian had in the end
= 220 - 160
= 60

Answer(s): 60