Archie and Sabrina has some money each. If Sabrina gives Archie $17, he will have 5 times as much money as her. If Archie gives Sabrina $18, he will have the same amount of money as her. How much money does each person have respectively?
- Archie?
- Sabrina?
| |
Case 1 |
Case 2 |
| |
Archie |
Sabrina |
Archie |
Sabrina |
| Before |
5 u - 17 |
1 u + 17 |
3 u + 18 |
3 u - 18 |
| Change |
+ 17 |
- 17 |
- 18 |
+ 18 |
| After |
5 u |
1 u |
3 u |
3 u |
(a)
If Sabrina gives Archie some money or Archie gives Sabrina some money, the total amount of money remains the same.
Total amount that Archie and Sabrina have in the end for both cases
= 5 u + 1 u
= 6 u
Amount that Archie and Sabrina each has in the end in Case 2
= 6 u ÷ 2
= 3 u
The amount that Archie has at first in Case 1 and Case 2 is the same.
5 u - 17 = 3 u + 18
5 u - 3 u = 18 + 17
1 u = 35
Amount that Archie has
= 3 u + 18
= 3 x 35 + 18
= 105 + 18
= $123
(b)
Amount that Sabrina has
= 1 u + 17
= 35 + 17
= $52
Answer(s): (a) $123; (b) $52
