Zane bought 100 white and yellow balloons for a party. The number of yellow balloons was ³₇ times as many as the number of white balloons. Zane used ¹₃ times as many yellow balloons as white balloons and was left with twice as many yellow balloons as white balloons. How many balloons did Zane have in the end?

	Yellow (1)	White (2)	Make b the same. (2)x2 = (3)
Before	30	70	140
Change	- 1 p	- 3 p	- 6 p
After	2 b	1 b	2 b

Number of yellow balloons that Zane bought at first = 3 u
Number of white balloons that Zane bought at first = 7 u

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

10 u = 100

1 u = 100 ÷ 10 = 10

Number of yellow balloons at first
= 3 u
= 3 x 10
= 30

Number of white balloons at first
= 7 u
= 7 x 10
= 70

30 - 1 p = 2 b --- (1)
70 - 3 p = 1 b --- (2)

(2)_x2
140 - 6 p = 2 b --- (3)

(3) = (1)
140 - 6 p = 30 - 1 p
6 p - 1 p = 140 - 30 
5 p = 110

1 p = 110 ÷ 5 = 22

Number of balloons that Zane used
= 1 p + 3 p
= 4 p
= 4 x 22
= 88

Number of balloons that Zane had in the end
= 100 - 88
= 12

Answer(s): 12