Tommy bought 198 purple and blue balloons for a party. The number of blue balloons was ⁴₇ times as many as the number of purple balloons. Tommy used ¹₃ times as many blue balloons as purple balloons and was left with twice as many blue balloons as purple balloons. How many balloons did Tommy have in the end?

	Blue (1)	Purple (2)	Make b the same. (2)x2 = (3)
Before	72	126	252
Change	- 1 p	- 3 p	- 6 p
After	2 b	1 b	2 b

Number of blue balloons that Tommy bought at first = 4 u
Number of purple balloons that Tommy bought at first = 7 u

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

11 u = 198

1 u = 198 ÷ 11 = 18

Number of blue balloons at first
= 4 u
= 4 x 18
= 72

Number of purple balloons at first
= 7 u
= 7 x 18
= 126

72 - 1 p = 2 b --- (1)
126 - 3 p = 1 b --- (2)

(2)_x2
252 - 6 p = 2 b --- (3)

(3) = (1)
252 - 6 p = 72 - 1 p
6 p - 1 p = 252 - 72 
5 p = 180

1 p = 180 ÷ 5 = 36

Number of balloons that Tommy used
= 1 p + 3 p
= 4 p
= 4 x 36
= 144

Number of balloons that Tommy had in the end
= 198 - 144
= 54

Answer(s): 54