Gabriel and Dana has some money each. If Dana gives Gabriel $15, he will have 5 times as much money as her. If Gabriel gives Dana $19, he will have the same amount of money as her. How much money does each person have respectively?
- Gabriel?
- Dana?
| |
Case 1 |
Case 2 |
| |
Gabriel |
Dana |
Gabriel |
Dana |
| Before |
5 u - 15 |
1 u + 15 |
3 u + 19 |
3 u - 19 |
| Change |
+ 15 |
- 15 |
- 19 |
+ 19 |
| After |
5 u |
1 u |
3 u |
3 u |
(a)
If Dana gives Gabriel some money or Gabriel gives Dana some money, the total amount of money remains the same.
Total amount that Gabriel and Dana have in the end for both cases
= 5 u + 1 u
= 6 u
Amount that Gabriel and Dana each has in the end in Case 2
= 6 u ÷ 2
= 3 u
The amount that Gabriel has at first in Case 1 and Case 2 is the same.
5 u - 15 = 3 u + 19
5 u - 3 u = 19 + 15
1 u = 34
Amount that Gabriel has
= 3 u + 19
= 3 x 34 + 19
= 102 + 19
= $121
(b)
Amount that Dana has
= 1 u + 15
= 34 + 15
= $49
Answer(s): (a) $121; (b) $49
