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

	Pink (1)	Grey (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 Vaidev bought at first = 4 u
Number of grey balloons that Vaidev 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 grey 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 Vaidev used
= 1 p + 4 p
= 5 p
= 5 x 11
= 55

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

Answer(s): 44