Paul bought 88 blue and purple balloons for a party. The number of purple balloons was ³₅ times as many as the number of blue balloons. Paul used ¹₄ times as many purple balloons as blue balloons and was left with thrice as many purple balloons as blue balloons. How many balloons did Paul have in the end?

	Purple (1)	Blue (2)	Make b the same. (2)x3 = (3)
Before	33	55	165
Change	- 1 p	- 4 p	- 12 p
After	3 b	1 b	3 b

Number of purple balloons that Paul bought at first = 3 u
Number of blue balloons that Paul 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 purple balloons at first
= 3 u
= 3 x 11
= 33

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

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

(2)_x3
165 - 12 p = 3 b --- (3)

(3) = (1)
165 - 12 p = 33 - 1 p
12 p - 1 p = 165 - 33 
11 p = 132

1 p = 132 ÷ 11 = 12

Number of balloons that Paul used
= 1 p + 4 p
= 5 p
= 5 x 12
= 60

Number of balloons that Paul had in the end
= 88 - 60
= 28

Answer(s): 28