Pierre and Xuan has some money each. If Xuan gives Pierre $12, he will have 5 times as much money as her. If Pierre gives Xuan $15, he will have the same amount of money as her. How much money does each person have respectively?
- Pierre?
- Xuan?
|
Case 1 |
Case 2 |
|
Pierre |
Xuan |
Pierre |
Xuan |
Before |
5 u - 12 |
1 u + 12 |
3 u + 15 |
3 u - 15 |
Change |
+ 12 |
- 12 |
- 15 |
+ 15 |
After |
5 u |
1 u |
3 u |
3 u |
(a)
If Xuan gives Pierre some money or Pierre gives Xuan some money, the total amount of money remains the same.
Total amount that Pierre and Xuan have in the end for both cases
= 5 u + 1 u
= 6 u
Amount that Pierre and Xuan each has in the end in Case 2
= 6 u ÷ 2
= 3 u
The amount that Pierre has at first in Case 1 and Case 2 is the same.
5 u - 12 = 3 u + 15
5 u - 3 u = 15 + 12
1 u = 27
Amount that Pierre has
= 3 u + 15
= 3 x 27 + 15
= 81 + 15
= $96
(b)
Amount that Xuan has
= 1 u + 12
= 27 + 12
= $39
Answer(s): (a) $96; (b) $39