Nick bought 136 grey and purple balloons for a party. The number of purple balloons was ³₅ times as many as the number of grey balloons. Nick used ¹₄ times as many purple balloons as grey balloons and was left with twice as many purple balloons as grey balloons. How many balloons did Nick have in the end?

	Purple (1)	Grey (2)	Make b the same. (2)x2 = (3)
Before	51	85	170
Change	- 1 p	- 4 p	- 8 p
After	2 b	1 b	2 b

Number of purple balloons that Nick bought at first = 3 u
Number of grey balloons that Nick bought at first = 5 u

Total number of balloons at first
= 3 u + 5 u
= 8 u

8 u = 136

1 u = 136 ÷ 8 = 17

Number of purple balloons at first
= 3 u
= 3 x 17
= 51

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

51 - 1 p = 2 b --- (1)
85 - 4 p = 1 b --- (2)

(2)_x2
170 - 8 p = 2 b --- (3)

(3) = (1)
170 - 8 p = 51 - 1 p
8 p - 1 p = 170 - 51 
7 p = 119

1 p = 119 ÷ 7 = 17

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

Number of balloons that Nick had in the end
= 136 - 85
= 51

Answer(s): 51