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

	Yellow (1)	Silver (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 yellow balloons that Oliver bought at first = 4 u
Number of silver balloons that Oliver 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 yellow balloons at first
= 4 u
= 4 x 16
= 64

Number of silver 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 Oliver used
= 1 p + 3 p
= 4 p
= 4 x 32
= 128

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

Answer(s): 48