Ken bought 88 grey and black balloons for a party. The number of black balloons was ³₅ times as many as the number of grey balloons. Ken used ¹₃ times as many black balloons as grey balloons and was left with four times as many black balloons as grey balloons. How many balloons did Ken have in the end?

	Black (1)	Grey (2)	Make b the same. (2)x4 = (3)
Before	33	55	220
Change	- 1 p	- 3 p	- 12 p
After	4 b	1 b	4 b

Number of black balloons that Ken bought at first = 3 u
Number of grey balloons that Ken bought at first = 5 u

Total number of balloons at first
= 3 u + 5 u
= 8 u

8 u = 88

1 u = 88 ÷ 8 = 11

Number of black balloons at first
= 3 u
= 3 x 11
= 33

Number of grey balloons at first
= 5 u
= 5 x 11
= 55

33 - 1 p = 4 b --- (1)
55 - 3 p = 1 b --- (2)

(2)_x4
220 - 12 p = 4 b --- (3)

(3) = (1)
220 - 12 p = 33 - 1 p
12 p - 1 p = 220 - 33 
11 p = 187

1 p = 187 ÷ 11 = 17

Number of balloons that Ken used
= 1 p + 3 p
= 4 p
= 4 x 17
= 68

Number of balloons that Ken had in the end
= 88 - 68
= 20

Answer(s): 20