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

	Grey (1)	White (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 grey balloons that Harry bought at first = 4 u
Number of white balloons that Harry 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 grey balloons at first
= 4 u
= 4 x 17
= 68

Number of white 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 Harry used
= 1 p + 3 p
= 4 p
= 4 x 34
= 136

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

Answer(s): 51