Zeph bought 77 purple and black balloons for a party. The number of black balloons was ²₅ times as many as the number of purple balloons. Zeph used ¹₄ times as many black balloons as purple balloons and was left with thrice as many black balloons as purple balloons. How many balloons did Zeph have in the end?

	Black (1)	Purple (2)	Make b the same. (2)x3 = (3)
Before	22	55	165
Change	- 1 p	- 4 p	- 12 p
After	3 b	1 b	3 b

Number of black balloons that Zeph bought at first = 2 u
Number of purple balloons that Zeph bought at first = 5 u

Total number of balloons at first
= 2 u + 5 u
= 7 u

7 u = 77

1 u = 77 ÷ 7 = 11

Number of black balloons at first
= 2 u
= 2 x 11
= 22

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

22 - 1 p = 3 b --- (1)
55 - 4 p = 1 b --- (2)

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

(3) = (1)
165 - 12 p = 22 - 1 p
12 p - 1 p = 165 - 22 
11 p = 143

1 p = 143 ÷ 11 = 13

Number of balloons that Zeph used
= 1 p + 4 p
= 5 p
= 5 x 13
= 65

Number of balloons that Zeph had in the end
= 77 - 65
= 12

Answer(s): 12