Cody and Xuan has some money each. If Xuan gives Cody $19, he will have 3 times as much money as her. If Cody gives Xuan $14, he will have the same amount of money as her. How much money does each person have respectively?
- Cody?
- Xuan?
| |
Case 1 |
Case 2 |
| |
Cody |
Xuan |
Cody |
Xuan |
| Before |
3 u - 19 |
1 u + 19 |
2 u + 14 |
2 u - 14 |
| Change |
+ 19 |
- 19 |
- 14 |
+ 14 |
| After |
3 u |
1 u |
2 u |
2 u |
(a)
If Xuan gives Cody some money or Cody gives Xuan some money, the total amount of money remains the same.
Total amount that Cody and Xuan have in the end for both cases
= 3 u + 1 u
= 4 u
Amount that Cody and Xuan each has in the end in Case 2
= 4 u ÷ 2
= 2 u
The amount that Cody has at first in Case 1 and Case 2 is the same.
3 u - 19 = 2 u + 14
3 u - 2 u = 14 + 19
1 u = 33
Amount that Cody has
= 2 u + 14
= 2 x 33 + 14
= 66 + 14
= $80
(b)
Amount that Xuan has
= 1 u + 19
= 33 + 19
= $52
Answer(s): (a) $80; (b) $52
