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

	Pink (1)	Blue (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 pink balloons that Fabian bought at first = 4 u
Number of blue balloons that Fabian 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 pink balloons at first
= 4 u
= 4 x 10
= 40

Number of blue 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 Fabian used
= 1 p + 3 p
= 4 p
= 4 x 12
= 48

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

Answer(s): 42