Jenson bought 135 silver and black balloons for a party. The number of black balloons was ⁴₅ times as many as the number of silver balloons. Jenson used ¹₄ times as many black balloons as silver balloons and was left with thrice as many black balloons as silver balloons. How many balloons did Jenson have in the end?

	Black (1)	Silver (2)	Make b the same. (2)x3 = (3)
Before	60	75	225
Change	- 1 p	- 4 p	- 12 p
After	3 b	1 b	3 b

Number of black balloons that Jenson bought at first = 4 u
Number of silver balloons that Jenson bought at first = 5 u

Total number of balloons at first
= 4 u + 5 u
= 9 u

9 u = 135

1 u = 135 ÷ 9 = 15

Number of black balloons at first
= 4 u
= 4 x 15
= 60

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

60 - 1 p = 3 b --- (1)
75 - 4 p = 1 b --- (2)

(2)_x3
225 - 12 p = 3 b --- (3)

(3) = (1)
225 - 12 p = 60 - 1 p
12 p - 1 p = 225 - 60 
11 p = 165

1 p = 165 ÷ 11 = 15

Number of balloons that Jenson used
= 1 p + 4 p
= 5 p
= 5 x 15
= 75

Number of balloons that Jenson had in the end
= 135 - 75
= 60

Answer(s): 60