Jenson bought 120 red and pink balloons for a party. The number of pink balloons was ³₅ times as many as the number of red balloons. Jenson used ¹₂ times as many pink balloons as red balloons and was left with thrice as many pink balloons as red balloons. How many balloons did Jenson have in the end?

	Pink (1)	Red (2)	Make b the same. (2)x3 = (3)
Before	45	75	225
Change	- 1 p	- 2 p	- 6 p
After	3 b	1 b	3 b

Number of pink balloons that Jenson bought at first = 3 u
Number of red balloons that Jenson 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 pink balloons at first
= 3 u
= 3 x 15
= 45

Number of red balloons at first
= 5 u
= 5 x 15
= 75

45 - 1 p = 3 b --- (1)
75 - 2 p = 1 b --- (2)

(2)_x3
225 - 6 p = 3 b --- (3)

(3) = (1)
225 - 6 p = 45 - 1 p
6 p - 1 p = 225 - 45 
5 p = 180

1 p = 180 ÷ 5 = 36

Number of balloons that Jenson used
= 1 p + 2 p
= 3 p
= 3 x 36
= 108

Number of balloons that Jenson had in the end
= 120 - 108
= 12

Answer(s): 12