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

	Gold (1)	Blue (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 gold balloons that Bobby bought at first = 4 u
Number of blue balloons that Bobby 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 gold balloons at first
= 4 u
= 4 x 16
= 64

Number of blue 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 Bobby used
= 1 p + 3 p
= 4 p
= 4 x 32
= 128

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

Answer(s): 48