Jack bought 99 green and yellow balloons for a party. The number of yellow balloons was ⁴₅ times as many as the number of green balloons. Jack used ¹₃ times as many yellow balloons as green balloons and was left with four times as many yellow balloons as green balloons. How many balloons did Jack have in the end?

	Yellow (1)	Green (2)	Make b the same. (2)x4 = (3)
Before	44	55	220
Change	- 1 p	- 3 p	- 12 p
After	4 b	1 b	4 b

Number of yellow balloons that Jack bought at first = 4 u
Number of green balloons that Jack bought at first = 5 u

Total number of balloons at first
= 4 u + 5 u
= 9 u

9 u = 99

1 u = 99 ÷ 9 = 11

Number of yellow balloons at first
= 4 u
= 4 x 11
= 44

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

44 - 1 p = 4 b --- (1)
55 - 3 p = 1 b --- (2)

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

(3) = (1)
220 - 12 p = 44 - 1 p
12 p - 1 p = 220 - 44 
11 p = 176

1 p = 176 ÷ 11 = 16

Number of balloons that Jack used
= 1 p + 3 p
= 4 p
= 4 x 16
= 64

Number of balloons that Jack had in the end
= 99 - 64
= 35

Answer(s): 35