Dylan bought 112 yellow and grey balloons for a party. The number of grey balloons was ³₅ times as many as the number of yellow balloons. Dylan used ¹₄ times as many grey balloons as yellow balloons and was left with twice as many grey balloons as yellow balloons. How many balloons did Dylan have in the end?

	Grey (1)	Yellow (2)	Make b the same. (2)x2 = (3)
Before	42	70	140
Change	- 1 p	- 4 p	- 8 p
After	2 b	1 b	2 b

Number of grey balloons that Dylan bought at first = 3 u
Number of yellow balloons that Dylan 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 grey balloons at first
= 3 u
= 3 x 14
= 42

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

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

(2)_x2
140 - 8 p = 2 b --- (3)

(3) = (1)
140 - 8 p = 42 - 1 p
8 p - 1 p = 140 - 42 
7 p = 98

1 p = 98 ÷ 7 = 14

Number of balloons that Dylan used
= 1 p + 4 p
= 5 p
= 5 x 14
= 70

Number of balloons that Dylan had in the end
= 112 - 70
= 42

Answer(s): 42