Archie and Esther has some money each. If Esther gives Archie $18, he will have 7 times as much money as her. If Archie gives Esther $17, he will have the same amount of money as her. How much money does each person have respectively?

1. Archie?
2. Esther?

	Case 1		Case 2
	Archie	Esther	Archie	Esther
Before	7 u - 18	1 u + 18	4 u + 17	4 u - 17
Change	+ 18	- 18	- 17	+ 17
After	7 u	1 u	4 u	4 u

(a)
If Esther gives Archie some money or Archie gives Esther some money, the total amount of money remains the same.  

Total amount that Archie and Esther have in the end for both cases
= 7 u + 1 u
= 8 u

Amount that Archie and Esther each has in the end in Case 2
= 8 u ÷ 2
= 4 u

The amount that Archie has at first in Case 1 and Case 2 is the same.
7 u - 18 = 4 u + 17
7 u - 4 u = 17 + 18

1 u = 35

Amount that Archie has
= 4 u + 17
= 4 x 35 + 17
= 140 + 17
= $157

(b)
Amount that Esther has
= 1 u + 18
= 35 + 18
= $53

Answer(s): (a) $157; (b) $53