Sam bought 165 blue and pink balloons for a party. The number of pink balloons was ⁴₇ times as many as the number of blue balloons. Sam used ¹₃ times as many pink balloons as blue balloons and was left with twice as many pink balloons as blue balloons. How many balloons did Sam have in the end?

	Pink (1)	Blue (2)	Make b the same. (2)x2 = (3)
Before	60	105	210
Change	- 1 p	- 3 p	- 6 p
After	2 b	1 b	2 b

Number of pink balloons that Sam bought at first = 4 u
Number of blue balloons that Sam bought at first = 7 u

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

11 u = 165

1 u = 165 ÷ 11 = 15

Number of pink balloons at first
= 4 u
= 4 x 15
= 60

Number of blue balloons at first
= 7 u
= 7 x 15
= 105

60 - 1 p = 2 b --- (1)
105 - 3 p = 1 b --- (2)

(2)_x2
210 - 6 p = 2 b --- (3)

(3) = (1)
210 - 6 p = 60 - 1 p
6 p - 1 p = 210 - 60 
5 p = 150

1 p = 150 ÷ 5 = 30

Number of balloons that Sam used
= 1 p + 3 p
= 4 p
= 4 x 30
= 120

Number of balloons that Sam had in the end
= 165 - 120
= 45

Answer(s): 45