Olivia and Winnie have some puffs each. If Olivia gives Winnie 18 puffs, Olivia will have ⁶₇ as many puffs as Winnie. If Olivia gives Winnie 15 puffs, they will have an equal number of puffs. How many puffs does Olivia have at first?

	Case 1		Case 2
	Olivia	Winnie	Olivia	Winnie
Before	6 u + 18	7 u - 18	6.5 u + 15	6.5 u - 15
Change	- 18	+ 18	- 15	+ 15
After	6 u	7 u	6.5 u	6.5 u

Total number of puffs that Olivia and Winnie have
= 6 u + 7 u
= 13 u 

Number of puffs that Olivia and Winnie each has in the end is the same.

Number of puffs that Olivia and Winnie each has in the end in Case 2
= 13 u ÷ 2
= 6.5 u

Number of puffs that Olivia had at first is the same in Case 1 and Case 2.

6.5 u + 15 = 6 u + 18
6.5 u - 6 u = 18 - 15
0.5 u = 3

1 u = 3 ÷ 0.5 = 6

Number of puffs that Olivia has
= 6 u + 18
= 6 x 6 + 18
= 36 + 18
= 54

Answer(s): 54