Archie bought 144 black and red balloons for a party. The number of red balloons was ³₅ times as many as the number of black balloons. Archie used ¹₄ times as many red balloons as black balloons and was left with twice as many red balloons as black balloons. How many balloons did Archie have in the end?

	Red (1)	Black (2)	Make b the same. (2)x2 = (3)
Before	54	90	180
Change	- 1 p	- 4 p	- 8 p
After	2 b	1 b	2 b

Number of red balloons that Archie bought at first = 3 u
Number of black balloons that Archie bought at first = 5 u

Total number of balloons at first
= 3 u + 5 u
= 8 u

8 u = 144

1 u = 144 ÷ 8 = 18

Number of red balloons at first
= 3 u
= 3 x 18
= 54

Number of black balloons at first
= 5 u
= 5 x 18
= 90

54 - 1 p = 2 b --- (1)
90 - 4 p = 1 b --- (2)

(2)_x2
180 - 8 p = 2 b --- (3)

(3) = (1)
180 - 8 p = 54 - 1 p
8 p - 1 p = 180 - 54 
7 p = 126

1 p = 126 ÷ 7 = 18

Number of balloons that Archie used
= 1 p + 4 p
= 5 p
= 5 x 18
= 90

Number of balloons that Archie had in the end
= 144 - 90
= 54

Answer(s): 54