Tommy bought 135 yellow and red balloons for a party. The number of red balloons was ⁴₅ times as many as the number of yellow balloons. Tommy used ¹₂ times as many red balloons as yellow balloons and was left with thrice as many red balloons as yellow balloons. How many balloons did Tommy have in the end?

	Red (1)	Yellow (2)	Make b the same. (2)x3 = (3)
Before	60	75	225
Change	- 1 p	- 2 p	- 6 p
After	3 b	1 b	3 b

Number of red balloons that Tommy bought at first = 4 u
Number of yellow balloons that Tommy bought at first = 5 u

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

9 u = 135

1 u = 135 ÷ 9 = 15

Number of red balloons at first
= 4 u
= 4 x 15
= 60

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

60 - 1 p = 3 b --- (1)
75 - 2 p = 1 b --- (2)

(2)_x3
225 - 6 p = 3 b --- (3)

(3) = (1)
225 - 6 p = 60 - 1 p
6 p - 1 p = 225 - 60 
5 p = 165

1 p = 165 ÷ 5 = 33

Number of balloons that Tommy used
= 1 p + 2 p
= 3 p
= 3 x 33
= 99

Number of balloons that Tommy had in the end
= 135 - 99
= 36

Answer(s): 36