Andy bought 105 gold and white balloons for a party. The number of white balloons was ²₅ times as many as the number of gold balloons. Andy used ¹₃ times as many white balloons as gold balloons and was left with twice as many white balloons as gold balloons. How many balloons did Andy have in the end?

	White (1)	Gold (2)	Make b the same. (2)x2 = (3)
Before	30	75	150
Change	- 1 p	- 3 p	- 6 p
After	2 b	1 b	2 b

Number of white balloons that Andy bought at first = 2 u
Number of gold balloons that Andy bought at first = 5 u

Total number of balloons at first
= 2 u + 5 u
= 7 u

7 u = 105

1 u = 105 ÷ 7 = 15

Number of white balloons at first
= 2 u
= 2 x 15
= 30

Number of gold balloons at first
= 5 u
= 5 x 15
= 75

30 - 1 p = 2 b --- (1)
75 - 3 p = 1 b --- (2)

(2)_x2
150 - 6 p = 2 b --- (3)

(3) = (1)
150 - 6 p = 30 - 1 p
6 p - 1 p = 150 - 30 
5 p = 120

1 p = 120 ÷ 5 = 24

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

Number of balloons that Andy had in the end
= 105 - 96
= 9

Answer(s): 9