Caden bought 135 grey and pink balloons for a party. The number of pink balloons was ⁴₅ times as many as the number of grey balloons. Caden used ¹₄ times as many pink balloons as grey balloons and was left with thrice as many pink balloons as grey balloons. How many balloons did Caden have in the end?

	Pink (1)	Grey (2)	Make b the same. (2)x3 = (3)
Before	60	75	225
Change	- 1 p	- 4 p	- 12 p
After	3 b	1 b	3 b

Number of pink balloons that Caden bought at first = 4 u
Number of grey balloons that Caden 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 pink balloons at first
= 4 u
= 4 x 15
= 60

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

60 - 1 p = 3 b --- (1)
75 - 4 p = 1 b --- (2)

(2)_x3
225 - 12 p = 3 b --- (3)

(3) = (1)
225 - 12 p = 60 - 1 p
12 p - 1 p = 225 - 60 
11 p = 165

1 p = 165 ÷ 11 = 15

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

Number of balloons that Caden had in the end
= 135 - 75
= 60

Answer(s): 60