Harry bought 110 grey and white balloons for a party. The number of white balloons was ⁴₇ times as many as the number of grey balloons. Harry used ¹₂ times as many white balloons as grey balloons and was left with thrice as many white balloons as grey balloons. How many balloons did Harry have in the end?

	White (1)	Grey (2)	Make b the same. (2)x3 = (3)
Before	40	70	210
Change	- 1 p	- 2 p	- 6 p
After	3 b	1 b	3 b

Number of white balloons that Harry bought at first = 4 u
Number of grey balloons that Harry bought at first = 7 u

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

11 u = 110

1 u = 110 ÷ 11 = 10

Number of white balloons at first
= 4 u
= 4 x 10
= 40

Number of grey balloons at first
= 7 u
= 7 x 10
= 70

40 - 1 p = 3 b --- (1)
70 - 2 p = 1 b --- (2)

(2)_x3
210 - 6 p = 3 b --- (3)

(3) = (1)
210 - 6 p = 40 - 1 p
6 p - 1 p = 210 - 40 
5 p = 170

1 p = 170 ÷ 5 = 34

Number of balloons that Harry used
= 1 p + 2 p
= 3 p
= 3 x 34
= 102

Number of balloons that Harry had in the end
= 110 - 102
= 8

Answer(s): 8