Mary and Ivory have some shortbreads each. If Mary gives Ivory 30 shortbreads, Mary will have ¹₈ as many shortbreads as Ivory. If Mary gives Ivory 2 shortbreads, they will have an equal number of shortbreads. How many shortbreads does Ivory have at first?

	Case 1		Case 2
	Mary	Ivory	Mary	Ivory
Before	1 u + 30	8 u - 30	4.5 u + 2	4.5 u - 2
Change	- 30	+ 30	- 2	+ 2
After	1 u	8 u	4.5 u	4.5 u

Total number of shortbreads that Mary and Ivory have
= 1 u + 8 u
= 9 u 

Number of shortbreads that Mary and Ivory each has in the end is the same.

Number of shortbreads that Mary and Ivory each has in the end in Case 2
= 9 u ÷ 2
= 4.5 u

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

4.5 u + 2 = 1 u + 30
4.5 u - 1 u = 30 - 2
0.5 u = 28

1 u = 28 ÷ 0.5 = 56

Number of shortbreads that Ivory has
= 8 u - 30
= 8 x 56 - 30
= 448 - 30
= 418

Answer(s): 418