Nicole and Rachel have some shortbreads each. If Nicole gives Rachel 28 shortbreads, Nicole will have ²₅ as many shortbreads as Rachel. If Nicole gives Rachel 19 shortbreads, they will have an equal number of shortbreads. How many shortbreads does Nicole have at first?

	Case 1		Case 2
	Nicole	Rachel	Nicole	Rachel
Before	2 u + 28	5 u - 28	3.5 u + 19	3.5 u - 19
Change	- 28	+ 28	- 19	+ 19
After	2 u	5 u	3.5 u	3.5 u

Total number of shortbreads that Nicole and Rachel have
= 2 u + 5 u
= 7 u 

Number of shortbreads that Nicole and Rachel each has in the end is the same.

Number of shortbreads that Nicole and Rachel each has in the end in Case 2
= 7 u ÷ 2
= 3.5 u

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

3.5 u + 19 = 2 u + 28
3.5 u - 2 u = 28 - 19
0.5 u = 9

1 u = 9 ÷ 0.5 = 18

Number of shortbreads that Nicole has
= 2 u + 28
= 2 x 18 + 28
= 36 + 28
= 64

Answer(s): 64