Albert bought 77 red and purple balloons for a party. The number of purple balloons was ²₅ times as many as the number of red balloons. Albert used ¹₃ times as many purple balloons as red balloons and was left with four times as many purple balloons as red balloons. How many balloons did Albert have in the end?

	Purple (1)	Red (2)	Make b the same. (2)x4 = (3)
Before	22	55	220
Change	- 1 p	- 3 p	- 12 p
After	4 b	1 b	4 b

Number of purple balloons that Albert bought at first = 2 u
Number of red balloons that Albert 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 purple balloons at first
= 2 u
= 2 x 11
= 22

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

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

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

(3) = (1)
220 - 12 p = 22 - 1 p
12 p - 1 p = 220 - 22 
11 p = 198

1 p = 198 ÷ 11 = 18

Number of balloons that Albert used
= 1 p + 3 p
= 4 p
= 4 x 18
= 72

Number of balloons that Albert had in the end
= 77 - 72
= 5

Answer(s): 5