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

	Blue (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 blue balloons that Ivan bought at first = 2 u
Number of red balloons that Ivan 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 blue 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 Ivan used
= 1 p + 3 p
= 4 p
= 4 x 18
= 72

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

Answer(s): 5