Zoe and Hilda have some cookies each. If Zoe gives Hilda 36 cookies, Zoe will have ⁷₈ as many cookies as Hilda. If Zoe gives Hilda 10 cookies, they will have an equal number of cookies. How many cookies does Hilda have at first?

	Case 1		Case 2
	Zoe	Hilda	Zoe	Hilda
Before	7 u + 36	8 u - 36	7.5 u + 10	7.5 u - 10
Change	- 36	+ 36	- 10	+ 10
After	7 u	8 u	7.5 u	7.5 u

Total number of cookies that Zoe and Hilda have
= 7 u + 8 u
= 15 u 

Number of cookies that Zoe and Hilda each has in the end is the same.

Number of cookies that Zoe and Hilda each has in the end in Case 2
= 15 u ÷ 2
= 7.5 u

Number of cookies that Zoe had at first is the same in Case 1 and Case 2.

7.5 u + 10 = 7 u + 36
7.5 u - 7 u = 36 - 10
0.5 u = 26

1 u = 26 ÷ 0.5 = 52

Number of cookies that Hilda has
= 8 u - 36
= 8 x 52 - 36
= 416 - 36
= 380

Answer(s): 380