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

	Grey (1)	Blue (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 grey balloons that Julian bought at first = 3 u
Number of blue balloons that Julian 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 grey balloons at first
= 3 u
= 3 x 17
= 51

Number of blue 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 Julian used
= 1 p + 4 p
= 5 p
= 5 x 17
= 85

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

Answer(s): 51