Ivan bought 112 black and gold balloons for a party. The number of gold balloons was ³₅ times as many as the number of black balloons. Ivan used ¹₂ times as many gold balloons as black balloons and was left with four times as many gold balloons as black balloons. How many balloons did Ivan have in the end?

	Gold (1)	Black (2)	Make b the same. (2)x4 = (3)
Before	42	70	280
Change	- 1 p	- 2 p	- 8 p
After	4 b	1 b	4 b

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

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

8 u = 112

1 u = 112 ÷ 8 = 14

Number of gold balloons at first
= 3 u
= 3 x 14
= 42

Number of black balloons at first
= 5 u
= 5 x 14
= 70

42 - 1 p = 4 b --- (1)
70 - 2 p = 1 b --- (2)

(2)_x4
280 - 8 p = 4 b --- (3)

(3) = (1)
280 - 8 p = 42 - 1 p
8 p - 1 p = 280 - 42 
7 p = 238

1 p = 238 ÷ 7 = 34

Number of balloons that Ivan used
= 1 p + 2 p
= 3 p
= 3 x 34
= 102

Number of balloons that Ivan had in the end
= 112 - 102
= 10

Answer(s): 10