Sam and Betty has some money each. If Betty gives Sam $17, he will have 3 times as much money as her. If Sam gives Betty $20, he will have the same amount of money as her. How much money does each person have respectively?
- Sam?
- Betty?
|
Case 1 |
Case 2 |
|
Sam |
Betty |
Sam |
Betty |
Before |
3 u - 17 |
1 u + 17 |
2 u + 20 |
2 u - 20 |
Change |
+ 17 |
- 17 |
- 20 |
+ 20 |
After |
3 u |
1 u |
2 u |
2 u |
(a)
If Betty gives Sam some money or Sam gives Betty some money, the total amount of money remains the same.
Total amount that Sam and Betty have in the end for both cases
= 3 u + 1 u
= 4 u
Amount that Sam and Betty each has in the end in Case 2
= 4 u ÷ 2
= 2 u
The amount that Sam has at first in Case 1 and Case 2 is the same.
3 u - 17 = 2 u + 20
3 u - 2 u = 20 + 17
1 u = 37
Amount that Sam has
= 2 u + 20
= 2 x 37 + 20
= 74 + 20
= $94
(b)
Amount that Betty has
= 1 u + 17
= 37 + 17
= $54
Answer(s): (a) $94; (b) $54