Cole bought 110 yellow and brown balloons for a party. The number of brown balloons was ³₇ times as many as the number of yellow balloons. Cole used ¹₃ times as many brown balloons as yellow balloons and was left with four times as many brown balloons as yellow balloons. How many balloons did Cole have in the end?

	Brown (1)	Yellow (2)	Make b the same. (2)x4 = (3)
Before	33	77	308
Change	- 1 p	- 3 p	- 12 p
After	4 b	1 b	4 b

Number of brown balloons that Cole bought at first = 3 u
Number of yellow balloons that Cole bought at first = 7 u

Total number of balloons at first
= 3 u + 7 u
= 10 u

10 u = 110

1 u = 110 ÷ 10 = 11

Number of brown balloons at first
= 3 u
= 3 x 11
= 33

Number of yellow balloons at first
= 7 u
= 7 x 11
= 77

33 - 1 p = 4 b --- (1)
77 - 3 p = 1 b --- (2)

(2)_x4
308 - 12 p = 4 b --- (3)

(3) = (1)
308 - 12 p = 33 - 1 p
12 p - 1 p = 308 - 33 
11 p = 275

1 p = 275 ÷ 11 = 25

Number of balloons that Cole used
= 1 p + 3 p
= 4 p
= 4 x 25
= 100

Number of balloons that Cole had in the end
= 110 - 100
= 10

Answer(s): 10