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