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

	Silver (1)	Pink (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 silver balloons that Mark bought at first = 4 u
Number of pink balloons that Mark 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 silver balloons at first
= 4 u
= 4 x 11
= 44

Number of pink 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 Mark used
= 1 p + 3 p
= 4 p
= 4 x 16
= 64

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

Answer(s): 35