Caden bought 99 black and silver balloons for a party. The number of silver balloons was ²₇ times as many as the number of black balloons. Caden used ¹₄ times as many silver balloons as black balloons and was left with thrice as many silver balloons as black balloons. How many balloons did Caden have in the end?

	Silver (1)	Black (2)	Make b the same. (2)x3 = (3)
Before	22	77	231
Change	- 1 p	- 4 p	- 12 p
After	3 b	1 b	3 b

Number of silver balloons that Caden bought at first = 2 u
Number of black balloons that Caden bought at first = 7 u

Total number of balloons at first
= 2 u + 7 u
= 9 u

9 u = 99

1 u = 99 ÷ 9 = 11

Number of silver balloons at first
= 2 u
= 2 x 11
= 22

Number of black balloons at first
= 7 u
= 7 x 11
= 77

22 - 1 p = 3 b --- (1)
77 - 4 p = 1 b --- (2)

(2)_x3
231 - 12 p = 3 b --- (3)

(3) = (1)
231 - 12 p = 22 - 1 p
12 p - 1 p = 231 - 22 
11 p = 209

1 p = 209 ÷ 11 = 19

Number of balloons that Caden used
= 1 p + 4 p
= 5 p
= 5 x 19
= 95

Number of balloons that Caden had in the end
= 99 - 95
= 4

Answer(s): 4