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

	Purple (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 purple balloons that Caden bought at first = 4 u
Number of white balloons that Caden 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 purple 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 Caden used
= 1 p + 2 p
= 3 p
= 3 x 22
= 66

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

Answer(s): 24