Gwen and Nicole have some muffins each. If Gwen gives Nicole 18 muffins, Gwen will have ⁴₇ as many muffins as Nicole. If Gwen gives Nicole 7 muffins, they will have an equal number of muffins. How many muffins does Nicole have at first?

	Case 1		Case 2
	Gwen	Nicole	Gwen	Nicole
Before	4 u + 18	7 u - 18	5.5 u + 7	5.5 u - 7
Change	- 18	+ 18	- 7	+ 7
After	4 u	7 u	5.5 u	5.5 u

Total number of muffins that Gwen and Nicole have
= 4 u + 7 u
= 11 u 

Number of muffins that Gwen and Nicole each has in the end is the same.

Number of muffins that Gwen and Nicole each has in the end in Case 2
= 11 u ÷ 2
= 5.5 u

Number of muffins that Gwen had at first is the same in Case 1 and Case 2.

5.5 u + 7 = 4 u + 18
5.5 u - 4 u = 18 - 7
0.5 u = 11

1 u = 11 ÷ 0.5 = 22

Number of muffins that Nicole has
= 7 u - 18
= 7 x 22 - 18
= 154 - 18
= 136

Answer(s): 136