Henry bought 120 black and silver balloons for a party. The number of silver balloons was ³₅ times as many as the number of black balloons. Henry used ¹₂ times as many silver balloons as black balloons and was left with thrice as many silver balloons as black balloons. How many balloons did Henry have in the end?

	Silver (1)	Black (2)	Make b the same. (2)x3 = (3)
Before	45	75	225
Change	- 1 p	- 2 p	- 6 p
After	3 b	1 b	3 b

Number of silver balloons that Henry bought at first = 3 u
Number of black balloons that Henry bought at first = 5 u

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

8 u = 120

1 u = 120 ÷ 8 = 15

Number of silver balloons at first
= 3 u
= 3 x 15
= 45

Number of black balloons at first
= 5 u
= 5 x 15
= 75

45 - 1 p = 3 b --- (1)
75 - 2 p = 1 b --- (2)

(2)_x3
225 - 6 p = 3 b --- (3)

(3) = (1)
225 - 6 p = 45 - 1 p
6 p - 1 p = 225 - 45 
5 p = 180

1 p = 180 ÷ 5 = 36

Number of balloons that Henry used
= 1 p + 2 p
= 3 p
= 3 x 36
= 108

Number of balloons that Henry had in the end
= 120 - 108
= 12

Answer(s): 12