Riordan bought 198 silver and black balloons for a party. The number of black balloons was ⁴₇ times as many as the number of silver balloons. Riordan used ¹₂ times as many black balloons as silver balloons and was left with five times as many black balloons as silver balloons. How many balloons did Riordan have in the end?

	Black (1)	Silver (2)	Make b the same. (2)x5 = (3)
Before	72	126	630
Change	- 1 p	- 2 p	- 10 p
After	5 b	1 b	5 b

Number of black balloons that Riordan bought at first = 4 u
Number of silver balloons that Riordan bought at first = 7 u

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

11 u = 198

1 u = 198 ÷ 11 = 18

Number of black balloons at first
= 4 u
= 4 x 18
= 72

Number of silver balloons at first
= 7 u
= 7 x 18
= 126

72 - 1 p = 5 b --- (1)
126 - 2 p = 1 b --- (2)

(2)_x5
630 - 10 p = 5 b --- (3)

(3) = (1)
630 - 10 p = 72 - 1 p
10 p - 1 p = 630 - 72 
9 p = 558

1 p = 558 ÷ 9 = 62

Number of balloons that Riordan used
= 1 p + 2 p
= 3 p
= 3 x 62
= 186

Number of balloons that Riordan had in the end
= 198 - 186
= 12

Answer(s): 12