Oliver bought 180 grey and purple balloons for a party. The number of purple balloons was ⁴₅ times as many as the number of grey balloons. Oliver used ¹₄ times as many purple balloons as grey balloons and was left with thrice as many purple balloons as grey balloons. How many balloons did Oliver have in the end?

	Purple (1)	Grey (2)	Make b the same. (2)x3 = (3)
Before	80	100	300
Change	- 1 p	- 4 p	- 12 p
After	3 b	1 b	3 b

Number of purple balloons that Oliver bought at first = 4 u
Number of grey balloons that Oliver bought at first = 5 u

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

9 u = 180

1 u = 180 ÷ 9 = 20

Number of purple balloons at first
= 4 u
= 4 x 20
= 80

Number of grey balloons at first
= 5 u
= 5 x 20
= 100

80 - 1 p = 3 b --- (1)
100 - 4 p = 1 b --- (2)

(2)_x3
300 - 12 p = 3 b --- (3)

(3) = (1)
300 - 12 p = 80 - 1 p
12 p - 1 p = 300 - 80 
11 p = 220

1 p = 220 ÷ 11 = 20

Number of balloons that Oliver used
= 1 p + 4 p
= 5 p
= 5 x 20
= 100

Number of balloons that Oliver had in the end
= 180 - 100
= 80

Answer(s): 80