Gabriel and Ivory has some money each. If Ivory gives Gabriel $14, he will have 5 times as much money as her. If Gabriel gives Ivory $17, he will have the same amount of money as her. How much money does each person have respectively?
- Gabriel?
- Ivory?
| |
Case 1 |
Case 2 |
| |
Gabriel |
Ivory |
Gabriel |
Ivory |
| Before |
5 u - 14 |
1 u + 14 |
3 u + 17 |
3 u - 17 |
| Change |
+ 14 |
- 14 |
- 17 |
+ 17 |
| After |
5 u |
1 u |
3 u |
3 u |
(a)
If Ivory gives Gabriel some money or Gabriel gives Ivory some money, the total amount of money remains the same.
Total amount that Gabriel and Ivory have in the end for both cases
= 5 u + 1 u
= 6 u
Amount that Gabriel and Ivory 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 - 14 = 3 u + 17
5 u - 3 u = 17 + 14
1 u = 31
Amount that Gabriel has
= 3 u + 17
= 3 x 31 + 17
= 93 + 17
= $110
(b)
Amount that Ivory has
= 1 u + 14
= 31 + 14
= $45
Answer(s): (a) $110; (b) $45
