Tommy bought 187 black and silver balloons for a party. The number of silver balloons was ⁴₇ times as many as the number of black balloons. Tommy used ¹₃ times as many silver balloons as black balloons and was left with twice as many silver balloons as black balloons. How many balloons did Tommy have in the end?

	Silver (1)	Black (2)	Make b the same. (2)x2 = (3)
Before	68	119	238
Change	- 1 p	- 3 p	- 6 p
After	2 b	1 b	2 b

Number of silver balloons that Tommy bought at first = 4 u
Number of black balloons that Tommy bought at first = 7 u

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

11 u = 187

1 u = 187 ÷ 11 = 17

Number of silver balloons at first
= 4 u
= 4 x 17
= 68

Number of black balloons at first
= 7 u
= 7 x 17
= 119

68 - 1 p = 2 b --- (1)
119 - 3 p = 1 b --- (2)

(2)_x2
238 - 6 p = 2 b --- (3)

(3) = (1)
238 - 6 p = 68 - 1 p
6 p - 1 p = 238 - 68 
5 p = 170

1 p = 170 ÷ 5 = 34

Number of balloons that Tommy used
= 1 p + 3 p
= 4 p
= 4 x 34
= 136

Number of balloons that Tommy had in the end
= 187 - 136
= 51

Answer(s): 51