Sam bought 154 white and silver balloons for a party. The number of silver balloons was ⁴₇ times as many as the number of white balloons. Sam used ¹₂ times as many silver balloons as white balloons and was left with four times as many silver balloons as white balloons. How many balloons did Sam have in the end?

	Silver (1)	White (2)	Make b the same. (2)x4 = (3)
Before	56	98	392
Change	- 1 p	- 2 p	- 8 p
After	4 b	1 b	4 b

Number of silver balloons that Sam bought at first = 4 u
Number of white balloons that Sam bought at first = 7 u

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

11 u = 154

1 u = 154 ÷ 11 = 14

Number of silver balloons at first
= 4 u
= 4 x 14
= 56

Number of white balloons at first
= 7 u
= 7 x 14
= 98

56 - 1 p = 4 b --- (1)
98 - 2 p = 1 b --- (2)

(2)_x4
392 - 8 p = 4 b --- (3)

(3) = (1)
392 - 8 p = 56 - 1 p
8 p - 1 p = 392 - 56 
7 p = 336

1 p = 336 ÷ 7 = 48

Number of balloons that Sam used
= 1 p + 2 p
= 3 p
= 3 x 48
= 144

Number of balloons that Sam had in the end
= 154 - 144
= 10

Answer(s): 10