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

	Pink (1)	Silver (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 pink balloons that Bobby bought at first = 4 u
Number of silver balloons that Bobby 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 pink balloons at first
= 4 u
= 4 x 20
= 80

Number of silver 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 Bobby used
= 1 p + 3 p
= 4 p
= 4 x 24
= 96

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

Answer(s): 84