Jack bought 80 red and grey balloons for a party. The number of grey balloons was ³₅ times as many as the number of red balloons. Jack used ¹₂ times as many grey balloons as red balloons and was left with thrice as many grey balloons as red balloons. How many balloons did Jack have in the end?

	Grey (1)	Red (2)	Make b the same. (2)x3 = (3)
Before	30	50	150
Change	- 1 p	- 2 p	- 6 p
After	3 b	1 b	3 b

Number of grey balloons that Jack bought at first = 3 u
Number of red balloons that Jack bought at first = 5 u

Total number of balloons at first
= 3 u + 5 u
= 8 u

8 u = 80

1 u = 80 ÷ 8 = 10

Number of grey balloons at first
= 3 u
= 3 x 10
= 30

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

30 - 1 p = 3 b --- (1)
50 - 2 p = 1 b --- (2)

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

(3) = (1)
150 - 6 p = 30 - 1 p
6 p - 1 p = 150 - 30 
5 p = 120

1 p = 120 ÷ 5 = 24

Number of balloons that Jack used
= 1 p + 2 p
= 3 p
= 3 x 24
= 72

Number of balloons that Jack had in the end
= 80 - 72
= 8

Answer(s): 8