Valen bought 96 white and grey balloons for a party. The number of grey balloons was ³₅ times as many as the number of white balloons. Valen used ¹₄ times as many grey balloons as white balloons and was left with twice as many grey balloons as white balloons. How many balloons did Valen have in the end?

	Grey (1)	White (2)	Make b the same. (2)x2 = (3)
Before	36	60	120
Change	- 1 p	- 4 p	- 8 p
After	2 b	1 b	2 b

Number of grey balloons that Valen bought at first = 3 u
Number of white balloons that Valen bought at first = 5 u

Total number of balloons at first
= 3 u + 5 u
= 8 u

8 u = 96

1 u = 96 ÷ 8 = 12

Number of grey balloons at first
= 3 u
= 3 x 12
= 36

Number of white balloons at first
= 5 u
= 5 x 12
= 60

36 - 1 p = 2 b --- (1)
60 - 4 p = 1 b --- (2)

(2)_x2
120 - 8 p = 2 b --- (3)

(3) = (1)
120 - 8 p = 36 - 1 p
8 p - 1 p = 120 - 36 
7 p = 84

1 p = 84 ÷ 7 = 12

Number of balloons that Valen used
= 1 p + 4 p
= 5 p
= 5 x 12
= 60

Number of balloons that Valen had in the end
= 96 - 60
= 36

Answer(s): 36