Reggie bought 135 gold and yellow balloons for a party. The number of yellow balloons was ⁴₅ times as many as the number of gold balloons. Reggie used ¹₃ times as many yellow balloons as gold balloons and was left with twice as many yellow balloons as gold balloons. How many balloons did Reggie have in the end?

	Yellow (1)	Gold (2)	Make b the same. (2)x2 = (3)
Before	60	75	150
Change	- 1 p	- 3 p	- 6 p
After	2 b	1 b	2 b

Number of yellow balloons that Reggie bought at first = 4 u
Number of gold balloons that Reggie bought at first = 5 u

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

9 u = 135

1 u = 135 ÷ 9 = 15

Number of yellow balloons at first
= 4 u
= 4 x 15
= 60

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

60 - 1 p = 2 b --- (1)
75 - 3 p = 1 b --- (2)

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

(3) = (1)
150 - 6 p = 60 - 1 p
6 p - 1 p = 150 - 60 
5 p = 90

1 p = 90 ÷ 5 = 18

Number of balloons that Reggie used
= 1 p + 3 p
= 4 p
= 4 x 18
= 72

Number of balloons that Reggie had in the end
= 135 - 72
= 63

Answer(s): 63