Andy bought 99 blue and pink balloons for a party. The number of pink balloons was ⁴₅ times as many as the number of blue balloons. Andy used ¹₄ times as many pink balloons as blue balloons and was left with thrice as many pink balloons as blue balloons. How many balloons did Andy have in the end?

	Pink (1)	Blue (2)	Make b the same. (2)x3 = (3)
Before	44	55	165
Change	- 1 p	- 4 p	- 12 p
After	3 b	1 b	3 b

Number of pink balloons that Andy bought at first = 4 u
Number of blue balloons that Andy bought at first = 5 u

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

9 u = 99

1 u = 99 ÷ 9 = 11

Number of pink balloons at first
= 4 u
= 4 x 11
= 44

Number of blue balloons at first
= 5 u
= 5 x 11
= 55

44 - 1 p = 3 b --- (1)
55 - 4 p = 1 b --- (2)

(2)_x3
165 - 12 p = 3 b --- (3)

(3) = (1)
165 - 12 p = 44 - 1 p
12 p - 1 p = 165 - 44 
11 p = 121

1 p = 121 ÷ 11 = 11

Number of balloons that Andy used
= 1 p + 4 p
= 5 p
= 5 x 11
= 55

Number of balloons that Andy had in the end
= 99 - 55
= 44

Answer(s): 44