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

	Blue (1)	Yellow (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 blue balloons that Ivan bought at first = 3 u
Number of yellow balloons that Ivan 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 blue balloons at first
= 3 u
= 3 x 11
= 33

Number of yellow 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 Ivan used
= 1 p + 3 p
= 4 p
= 4 x 17
= 68

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

Answer(s): 20