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

	Red (1)	Purple (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 red balloons that Oscar bought at first = 3 u
Number of purple balloons that Oscar 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 red balloons at first
= 3 u
= 3 x 17
= 51

Number of purple 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 Oscar used
= 1 p + 4 p
= 5 p
= 5 x 17
= 85

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

Answer(s): 51