Mark bought 126 pink and brown balloons for a party. The number of brown balloons was ⁴₅ times as many as the number of pink balloons. Mark used ¹₂ times as many brown balloons as pink balloons and was left with four times as many brown balloons as pink balloons. How many balloons did Mark have in the end?

	Brown (1)	Pink (2)	Make b the same. (2)x4 = (3)
Before	56	70	280
Change	- 1 p	- 2 p	- 8 p
After	4 b	1 b	4 b

Number of brown balloons that Mark bought at first = 4 u
Number of pink balloons that Mark bought at first = 5 u

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

9 u = 126

1 u = 126 ÷ 9 = 14

Number of brown balloons at first
= 4 u
= 4 x 14
= 56

Number of pink balloons at first
= 5 u
= 5 x 14
= 70

56 - 1 p = 4 b --- (1)
70 - 2 p = 1 b --- (2)

(2)_x4
280 - 8 p = 4 b --- (3)

(3) = (1)
280 - 8 p = 56 - 1 p
8 p - 1 p = 280 - 56 
7 p = 224

1 p = 224 ÷ 7 = 32

Number of balloons that Mark used
= 1 p + 2 p
= 3 p
= 3 x 32
= 96

Number of balloons that Mark had in the end
= 126 - 96
= 30

Answer(s): 30