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

	Blue (1)	Grey (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 blue balloons that Tom bought at first = 4 u
Number of grey balloons that Tom 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 blue balloons at first
= 4 u
= 4 x 17
= 68

Number of grey 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 Tom used
= 1 p + 3 p
= 4 p
= 4 x 34
= 136

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

Answer(s): 51