Will bought 90 grey and silver balloons for a party. The number of silver balloons was ⁴₅ times as many as the number of grey balloons. Will used ¹₃ times as many silver balloons as grey balloons and was left with twice as many silver balloons as grey balloons. How many balloons did Will have in the end?

	Silver (1)	Grey (2)	Make b the same. (2)x2 = (3)
Before	40	50	100
Change	- 1 p	- 3 p	- 6 p
After	2 b	1 b	2 b

Number of silver balloons that Will bought at first = 4 u
Number of grey balloons that Will bought at first = 5 u

Total number of balloons at first
= 4 u + 5 u
= 9 u

9 u = 90

1 u = 90 ÷ 9 = 10

Number of silver balloons at first
= 4 u
= 4 x 10
= 40

Number of grey balloons at first
= 5 u
= 5 x 10
= 50

40 - 1 p = 2 b --- (1)
50 - 3 p = 1 b --- (2)

(2)_x2
100 - 6 p = 2 b --- (3)

(3) = (1)
100 - 6 p = 40 - 1 p
6 p - 1 p = 100 - 40 
5 p = 60

1 p = 60 ÷ 5 = 12

Number of balloons that Will used
= 1 p + 3 p
= 4 p
= 4 x 12
= 48

Number of balloons that Will had in the end
= 90 - 48
= 42

Answer(s): 42