Nicole and Usha have some muffins each. If Nicole gives Usha 7 muffins, Nicole will have ⁴₅ as many muffins as Usha. If Nicole gives Usha 5 muffins, they will have an equal number of muffins. How many muffins does Nicole have at first?

	Case 1		Case 2
	Nicole	Usha	Nicole	Usha
Before	4 u + 7	5 u - 7	4.5 u + 5	4.5 u - 5
Change	- 7	+ 7	- 5	+ 5
After	4 u	5 u	4.5 u	4.5 u

Total number of muffins that Nicole and Usha have
= 4 u + 5 u
= 9 u 

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

Number of muffins that Nicole and Usha each has in the end in Case 2
= 9 u ÷ 2
= 4.5 u

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

4.5 u + 5 = 4 u + 7
4.5 u - 4 u = 7 - 5
0.5 u = 2

1 u = 2 ÷ 0.5 = 4

Number of muffins that Nicole has
= 4 u + 7
= 4 x 4 + 7
= 16 + 7
= 23

Answer(s): 23