Jeremy bought 209 blue and purple balloons for a party. The number of purple balloons was ⁴₇ times as many as the number of blue balloons. Jeremy used ¹₃ times as many purple balloons as blue balloons and was left with twice as many purple balloons as blue balloons. How many balloons did Jeremy have in the end?

	Purple (1)	Blue (2)	Make b the same. (2)x2 = (3)
Before	76	133	266
Change	- 1 p	- 3 p	- 6 p
After	2 b	1 b	2 b

Number of purple balloons that Jeremy bought at first = 4 u
Number of blue balloons that Jeremy bought at first = 7 u

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

11 u = 209

1 u = 209 ÷ 11 = 19

Number of purple balloons at first
= 4 u
= 4 x 19
= 76

Number of blue balloons at first
= 7 u
= 7 x 19
= 133

76 - 1 p = 2 b --- (1)
133 - 3 p = 1 b --- (2)

(2)_x2
266 - 6 p = 2 b --- (3)

(3) = (1)
266 - 6 p = 76 - 1 p
6 p - 1 p = 266 - 76 
5 p = 190

1 p = 190 ÷ 5 = 38

Number of balloons that Jeremy used
= 1 p + 3 p
= 4 p
= 4 x 38
= 152

Number of balloons that Jeremy had in the end
= 209 - 152
= 57

Answer(s): 57