Billy bought 112 grey and yellow balloons for a party. The number of yellow balloons was ³₅ times as many as the number of grey balloons. Billy used ¹₂ times as many yellow balloons as grey balloons and was left with four times as many yellow balloons as grey balloons. How many balloons did Billy have in the end?

	Yellow (1)	Grey (2)	Make b the same. (2)x4 = (3)
Before	42	70	280
Change	- 1 p	- 2 p	- 8 p
After	4 b	1 b	4 b

Number of yellow balloons that Billy bought at first = 3 u
Number of grey balloons that Billy bought at first = 5 u

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

8 u = 112

1 u = 112 ÷ 8 = 14

Number of yellow balloons at first
= 3 u
= 3 x 14
= 42

Number of grey balloons at first
= 5 u
= 5 x 14
= 70

42 - 1 p = 4 b --- (1)
70 - 2 p = 1 b --- (2)

(2)_x4
280 - 8 p = 4 b --- (3)

(3) = (1)
280 - 8 p = 42 - 1 p
8 p - 1 p = 280 - 42 
7 p = 238

1 p = 238 ÷ 7 = 34

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

Number of balloons that Billy had in the end
= 112 - 102
= 10

Answer(s): 10