Vincent bought 120 brown and silver balloons for a party. The number of silver balloons was ³₅ times as many as the number of brown balloons. Vincent used ¹₄ times as many silver balloons as brown balloons and was left with twice as many silver balloons as brown balloons. How many balloons did Vincent have in the end?

	Silver (1)	Brown (2)	Make b the same. (2)x2 = (3)
Before	45	75	150
Change	- 1 p	- 4 p	- 8 p
After	2 b	1 b	2 b

Number of silver balloons that Vincent bought at first = 3 u
Number of brown balloons that Vincent 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 brown balloons at first
= 5 u
= 5 x 15
= 75

45 - 1 p = 2 b --- (1)
75 - 4 p = 1 b --- (2)

(2)_x2
150 - 8 p = 2 b --- (3)

(3) = (1)
150 - 8 p = 45 - 1 p
8 p - 1 p = 150 - 45 
7 p = 105

1 p = 105 ÷ 7 = 15

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

Number of balloons that Vincent had in the end
= 120 - 75
= 45

Answer(s): 45