Henry bought 160 gold and black balloons for a party. The number of black balloons was ³₅ times as many as the number of gold balloons. Henry used ¹₃ times as many black balloons as gold balloons and was left with twice as many black balloons as gold balloons. How many balloons did Henry have in the end?

	Black (1)	Gold (2)	Make b the same. (2)x2 = (3)
Before	60	100	200
Change	- 1 p	- 3 p	- 6 p
After	2 b	1 b	2 b

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

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

8 u = 160

1 u = 160 ÷ 8 = 20

Number of black balloons at first
= 3 u
= 3 x 20
= 60

Number of gold balloons at first
= 5 u
= 5 x 20
= 100

60 - 1 p = 2 b --- (1)
100 - 3 p = 1 b --- (2)

(2)_x2
200 - 6 p = 2 b --- (3)

(3) = (1)
200 - 6 p = 60 - 1 p
6 p - 1 p = 200 - 60 
5 p = 140

1 p = 140 ÷ 5 = 28

Number of balloons that Henry used
= 1 p + 3 p
= 4 p
= 4 x 28
= 112

Number of balloons that Henry had in the end
= 160 - 112
= 48

Answer(s): 48