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

	Gold (1)	Blue (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 gold balloons that Oscar bought at first = 4 u
Number of blue balloons that Oscar 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 gold balloons at first
= 4 u
= 4 x 15
= 60

Number of blue 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 Oscar used
= 1 p + 4 p
= 5 p
= 5 x 15
= 75

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

Answer(s): 60