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

	Purple (1)	Silver (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 purple balloons that Liam bought at first = 3 u
Number of silver balloons that Liam 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 purple balloons at first
= 3 u
= 3 x 15
= 45

Number of silver 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 Liam used
= 1 p + 4 p
= 5 p
= 5 x 15
= 75

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

Answer(s): 45