Ethan bought 220 green and red balloons for a party. The number of red balloons was ⁴₇ times as many as the number of green balloons. Ethan used ¹₂ times as many red balloons as green balloons and was left with thrice as many red balloons as green balloons. How many balloons did Ethan have in the end?

	Red (1)	Green (2)	Make b the same. (2)x3 = (3)
Before	80	140	420
Change	- 1 p	- 2 p	- 6 p
After	3 b	1 b	3 b

Number of red balloons that Ethan bought at first = 4 u
Number of green balloons that Ethan 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 red balloons at first
= 4 u
= 4 x 20
= 80

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

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

(2)_x3
420 - 6 p = 3 b --- (3)

(3) = (1)
420 - 6 p = 80 - 1 p
6 p - 1 p = 420 - 80 
5 p = 340

1 p = 340 ÷ 5 = 68

Number of balloons that Ethan used
= 1 p + 2 p
= 3 p
= 3 x 68
= 204

Number of balloons that Ethan had in the end
= 220 - 204
= 16

Answer(s): 16