Albert bought 88 black and gold balloons for a party. The number of gold balloons was ³₅ times as many as the number of black balloons. Albert used ¹₄ times as many gold balloons as black balloons and was left with twice as many gold balloons as black balloons. How many balloons did Albert have in the end?

	Gold (1)	Black (2)	Make b the same. (2)x2 = (3)
Before	33	55	110
Change	- 1 p	- 4 p	- 8 p
After	2 b	1 b	2 b

Number of gold balloons that Albert bought at first = 3 u
Number of black balloons that Albert bought at first = 5 u

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

8 u = 88

1 u = 88 ÷ 8 = 11

Number of gold balloons at first
= 3 u
= 3 x 11
= 33

Number of black balloons at first
= 5 u
= 5 x 11
= 55

33 - 1 p = 2 b --- (1)
55 - 4 p = 1 b --- (2)

(2)_x2
110 - 8 p = 2 b --- (3)

(3) = (1)
110 - 8 p = 33 - 1 p
8 p - 1 p = 110 - 33 
7 p = 77

1 p = 77 ÷ 7 = 11

Number of balloons that Albert used
= 1 p + 4 p
= 5 p
= 5 x 11
= 55

Number of balloons that Albert had in the end
= 88 - 55
= 33

Answer(s): 33