Liam bought 176 gold and blue balloons for a party. The number of blue balloons was ⁴₇ times as many as the number of gold balloons. Liam used ¹₃ times as many blue balloons as gold balloons and was left with twice as many blue balloons as gold balloons. How many balloons did Liam have in the end?

	Blue (1)	Gold (2)	Make b the same. (2)x2 = (3)
Before	64	112	224
Change	- 1 p	- 3 p	- 6 p
After	2 b	1 b	2 b

Number of blue balloons that Liam bought at first = 4 u
Number of gold balloons that Liam bought at first = 7 u

Total number of balloons at first
= 4 u + 7 u
= 11 u

11 u = 176

1 u = 176 ÷ 11 = 16

Number of blue balloons at first
= 4 u
= 4 x 16
= 64

Number of gold balloons at first
= 7 u
= 7 x 16
= 112

64 - 1 p = 2 b --- (1)
112 - 3 p = 1 b --- (2)

(2)_x2
224 - 6 p = 2 b --- (3)

(3) = (1)
224 - 6 p = 64 - 1 p
6 p - 1 p = 224 - 64 
5 p = 160

1 p = 160 ÷ 5 = 32

Number of balloons that Liam used
= 1 p + 3 p
= 4 p
= 4 x 32
= 128

Number of balloons that Liam had in the end
= 176 - 128
= 48

Answer(s): 48