Owen bought 90 white and black balloons for a party. The number of black balloons was ⁴₅ times as many as the number of white balloons. Owen used ¹₂ times as many black balloons as white balloons and was left with thrice as many black balloons as white balloons. How many balloons did Owen have in the end?

	Black (1)	White (2)	Make b the same. (2)x3 = (3)
Before	40	50	150
Change	- 1 p	- 2 p	- 6 p
After	3 b	1 b	3 b

Number of black balloons that Owen bought at first = 4 u
Number of white balloons that Owen bought at first = 5 u

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

9 u = 90

1 u = 90 ÷ 9 = 10

Number of black balloons at first
= 4 u
= 4 x 10
= 40

Number of white balloons at first
= 5 u
= 5 x 10
= 50

40 - 1 p = 3 b --- (1)
50 - 2 p = 1 b --- (2)

(2)_x3
150 - 6 p = 3 b --- (3)

(3) = (1)
150 - 6 p = 40 - 1 p
6 p - 1 p = 150 - 40 
5 p = 110

1 p = 110 ÷ 5 = 22

Number of balloons that Owen used
= 1 p + 2 p
= 3 p
= 3 x 22
= 66

Number of balloons that Owen had in the end
= 90 - 66
= 24

Answer(s): 24