Gabriel and Jade has some money each. If Jade gives Gabriel $11, he will have 5 times as much money as her. If Gabriel gives Jade $19, he will have the same amount of money as her. How much money does each person have respectively?
- Gabriel?
- Jade?
|
Case 1 |
Case 2 |
|
Gabriel |
Jade |
Gabriel |
Jade |
Before |
5 u - 11 |
1 u + 11 |
3 u + 19 |
3 u - 19 |
Change |
+ 11 |
- 11 |
- 19 |
+ 19 |
After |
5 u |
1 u |
3 u |
3 u |
(a)
If Jade gives Gabriel some money or Gabriel gives Jade some money, the total amount of money remains the same.
Total amount that Gabriel and Jade have in the end for both cases
= 5 u + 1 u
= 6 u
Amount that Gabriel and Jade 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 - 11 = 3 u + 19
5 u - 3 u = 19 + 11
1 u = 30
Amount that Gabriel has
= 3 u + 19
= 3 x 30 + 19
= 90 + 19
= $109
(b)
Amount that Jade has
= 1 u + 11
= 30 + 11
= $41
Answer(s): (a) $109; (b) $41