Sam bought 132 white and green balloons for a party. The number of green balloons was ⁴₇ times as many as the number of white balloons. Sam used ¹₃ times as many green balloons as white balloons and was left with twice as many green balloons as white balloons. How many balloons did Sam have in the end?

	Green (1)	White (2)	Make b the same. (2)x2 = (3)
Before	48	84	168
Change	- 1 p	- 3 p	- 6 p
After	2 b	1 b	2 b

Number of green 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 = 132

1 u = 132 ÷ 11 = 12

Number of green balloons at first
= 4 u
= 4 x 12
= 48

Number of white balloons at first
= 7 u
= 7 x 12
= 84

48 - 1 p = 2 b --- (1)
84 - 3 p = 1 b --- (2)

(2)_x2
168 - 6 p = 2 b --- (3)

(3) = (1)
168 - 6 p = 48 - 1 p
6 p - 1 p = 168 - 48 
5 p = 120

1 p = 120 ÷ 5 = 24

Number of balloons that Sam used
= 1 p + 3 p
= 4 p
= 4 x 24
= 96

Number of balloons that Sam had in the end
= 132 - 96
= 36

Answer(s): 36