Luis bought 110 silver and blue balloons for a party. The number of blue balloons was ⁴₇ times as many as the number of silver balloons. Luis used ¹₂ times as many blue balloons as silver balloons and was left with thrice as many blue balloons as silver balloons. How many balloons did Luis have in the end?

	Blue (1)	Silver (2)	Make b the same. (2)x3 = (3)
Before	40	70	210
Change	- 1 p	- 2 p	- 6 p
After	3 b	1 b	3 b

Number of blue balloons that Luis bought at first = 4 u
Number of silver balloons that Luis bought at first = 7 u

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

11 u = 110

1 u = 110 ÷ 11 = 10

Number of blue balloons at first
= 4 u
= 4 x 10
= 40

Number of silver balloons at first
= 7 u
= 7 x 10
= 70

40 - 1 p = 3 b --- (1)
70 - 2 p = 1 b --- (2)

(2)_x3
210 - 6 p = 3 b --- (3)

(3) = (1)
210 - 6 p = 40 - 1 p
6 p - 1 p = 210 - 40 
5 p = 170

1 p = 170 ÷ 5 = 34

Number of balloons that Luis used
= 1 p + 2 p
= 3 p
= 3 x 34
= 102

Number of balloons that Luis had in the end
= 110 - 102
= 8

Answer(s): 8