Simon bought 135 black and silver balloons for a party. The number of silver balloons was ⁴₅ times as many as the number of black balloons. Simon used ¹₃ times as many silver balloons as black balloons and was left with twice as many silver balloons as black balloons. How many balloons did Simon have in the end?

	Silver (1)	Black (2)	Make b the same. (2)x2 = (3)
Before	60	75	150
Change	- 1 p	- 3 p	- 6 p
After	2 b	1 b	2 b

Number of silver balloons that Simon bought at first = 4 u
Number of black balloons that Simon 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 silver balloons at first
= 4 u
= 4 x 15
= 60

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

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

(2)_x2
150 - 6 p = 2 b --- (3)

(3) = (1)
150 - 6 p = 60 - 1 p
6 p - 1 p = 150 - 60 
5 p = 90

1 p = 90 ÷ 5 = 18

Number of balloons that Simon used
= 1 p + 3 p
= 4 p
= 4 x 18
= 72

Number of balloons that Simon had in the end
= 135 - 72
= 63

Answer(s): 63