Tim bought 144 black and yellow balloons for a party. The number of yellow balloons was ⁴₅ times as many as the number of black balloons. Tim used ¹₄ times as many yellow balloons as black balloons and was left with thrice as many yellow balloons as black balloons. How many balloons did Tim have in the end?

	Yellow (1)	Black (2)	Make b the same. (2)x3 = (3)
Before	64	80	240
Change	- 1 p	- 4 p	- 12 p
After	3 b	1 b	3 b

Number of yellow balloons that Tim bought at first = 4 u
Number of black balloons that Tim bought at first = 5 u

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

9 u = 144

1 u = 144 ÷ 9 = 16

Number of yellow balloons at first
= 4 u
= 4 x 16
= 64

Number of black balloons at first
= 5 u
= 5 x 16
= 80

64 - 1 p = 3 b --- (1)
80 - 4 p = 1 b --- (2)

(2)_x3
240 - 12 p = 3 b --- (3)

(3) = (1)
240 - 12 p = 64 - 1 p
12 p - 1 p = 240 - 64 
11 p = 176

1 p = 176 ÷ 11 = 16

Number of balloons that Tim used
= 1 p + 4 p
= 5 p
= 5 x 16
= 80

Number of balloons that Tim had in the end
= 144 - 80
= 64

Answer(s): 64