Japheth bought 180 yellow and black balloons for a party. The number of black balloons was ⁴₅ times as many as the number of yellow balloons. Japheth used ¹₃ times as many black balloons as yellow balloons and was left with twice as many black balloons as yellow balloons. How many balloons did Japheth have in the end?

	Black (1)	Yellow (2)	Make b the same. (2)x2 = (3)
Before	80	100	200
Change	- 1 p	- 3 p	- 6 p
After	2 b	1 b	2 b

Number of black balloons that Japheth bought at first = 4 u
Number of yellow balloons that Japheth bought at first = 5 u

Total number of balloons at first
= 4 u + 5 u
= 9 u

9 u = 180

1 u = 180 ÷ 9 = 20

Number of black balloons at first
= 4 u
= 4 x 20
= 80

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

80 - 1 p = 2 b --- (1)
100 - 3 p = 1 b --- (2)

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

(3) = (1)
200 - 6 p = 80 - 1 p
6 p - 1 p = 200 - 80 
5 p = 120

1 p = 120 ÷ 5 = 24

Number of balloons that Japheth used
= 1 p + 3 p
= 4 p
= 4 x 24
= 96

Number of balloons that Japheth had in the end
= 180 - 96
= 84

Answer(s): 84