Luis bought 120 black and pink balloons for a party. The number of pink balloons was ³₅ times as many as the number of black balloons. Luis used ¹₄ times as many pink balloons as black balloons and was left with twice as many pink balloons as black balloons. How many balloons did Luis have in the end?

	Pink (1)	Black (2)	Make b the same. (2)x2 = (3)
Before	45	75	150
Change	- 1 p	- 4 p	- 8 p
After	2 b	1 b	2 b

Number of pink balloons that Luis bought at first = 3 u
Number of black balloons that Luis bought at first = 5 u

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

8 u = 120

1 u = 120 ÷ 8 = 15

Number of pink balloons at first
= 3 u
= 3 x 15
= 45

Number of black balloons at first
= 5 u
= 5 x 15
= 75

45 - 1 p = 2 b --- (1)
75 - 4 p = 1 b --- (2)

(2)_x2
150 - 8 p = 2 b --- (3)

(3) = (1)
150 - 8 p = 45 - 1 p
8 p - 1 p = 150 - 45 
7 p = 105

1 p = 105 ÷ 7 = 15

Number of balloons that Luis used
= 1 p + 4 p
= 5 p
= 5 x 15
= 75

Number of balloons that Luis had in the end
= 120 - 75
= 45

Answer(s): 45