Ryan bought 120 yellow and grey balloons for a party. The number of grey balloons was ³₅ times as many as the number of yellow balloons. Ryan 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 Ryan have in the end?

	Grey (1)	Yellow (2)	Make b the same. (2)x2 = (3)
Before	45	75	150
Change	- 1 p	- 4 p	- 8 p
After	2 b	1 b	2 b

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

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

8 u = 120

1 u = 120 ÷ 8 = 15

Number of grey balloons at first
= 3 u
= 3 x 15
= 45

Number of yellow balloons at first
= 5 u
= 5 x 15
= 75

45 - 1 p = 2 b --- (1)
75 - 4 p = 1 b --- (2)

(2)_x2
150 - 8 p = 2 b --- (3)

(3) = (1)
150 - 8 p = 45 - 1 p
8 p - 1 p = 150 - 45 
7 p = 105

1 p = 105 ÷ 7 = 15

Number of balloons that Ryan used
= 1 p + 4 p
= 5 p
= 5 x 15
= 75

Number of balloons that Ryan had in the end
= 120 - 75
= 45

Answer(s): 45