Archie and Betty has some money each. If Betty gives Archie $19, he will have 7 times as much money as her. If Archie gives Betty $18, he will have the same amount of money as her. How much money does each person have respectively?
- Archie?
- Betty?
|
Case 1 |
Case 2 |
|
Archie |
Betty |
Archie |
Betty |
Before |
7 u - 19 |
1 u + 19 |
4 u + 18 |
4 u - 18 |
Change |
+ 19 |
- 19 |
- 18 |
+ 18 |
After |
7 u |
1 u |
4 u |
4 u |
(a)
If Betty gives Archie some money or Archie gives Betty some money, the total amount of money remains the same.
Total amount that Archie and Betty have in the end for both cases
= 7 u + 1 u
= 8 u
Amount that Archie and Betty 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 - 19 = 4 u + 18
7 u - 4 u = 18 + 19
1 u = 37
Amount that Archie has
= 4 u + 18
= 4 x 37 + 18
= 148 + 18
= $166
(b)
Amount that Betty has
= 1 u + 19
= 37 + 19
= $56
Answer(s): (a) $166; (b) $56