Sam bought 153 black and purple balloons for a party. The number of purple balloons was ⁴₅ times as many as the number of black balloons. Sam used ¹₄ times as many purple balloons as black balloons and was left with thrice as many purple balloons as black balloons. How many balloons did Sam have in the end?

	Purple (1)	Black (2)	Make b the same. (2)x3 = (3)
Before	68	85	255
Change	- 1 p	- 4 p	- 12 p
After	3 b	1 b	3 b

Number of purple balloons that Sam bought at first = 4 u
Number of black balloons that Sam bought at first = 5 u

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

9 u = 153

1 u = 153 ÷ 9 = 17

Number of purple balloons at first
= 4 u
= 4 x 17
= 68

Number of black balloons at first
= 5 u
= 5 x 17
= 85

68 - 1 p = 3 b --- (1)
85 - 4 p = 1 b --- (2)

(2)_x3
255 - 12 p = 3 b --- (3)

(3) = (1)
255 - 12 p = 68 - 1 p
12 p - 1 p = 255 - 68 
11 p = 187

1 p = 187 ÷ 11 = 17

Number of balloons that Sam used
= 1 p + 4 p
= 5 p
= 5 x 17
= 85

Number of balloons that Sam had in the end
= 153 - 85
= 68

Answer(s): 68