Ethan and Xylia has some money each. If Xylia gives Ethan $16, he will have 3 times as much money as her. If Ethan gives Xylia $12, he will have the same amount of money as her. How much money does each person have respectively?
- Ethan?
- Xylia?
|
Case 1 |
Case 2 |
|
Ethan |
Xylia |
Ethan |
Xylia |
Before |
3 u - 16 |
1 u + 16 |
2 u + 12 |
2 u - 12 |
Change |
+ 16 |
- 16 |
- 12 |
+ 12 |
After |
3 u |
1 u |
2 u |
2 u |
(a)
If Xylia gives Ethan some money or Ethan gives Xylia some money, the total amount of money remains the same.
Total amount that Ethan and Xylia have in the end for both cases
= 3 u + 1 u
= 4 u
Amount that Ethan and Xylia each has in the end in Case 2
= 4 u ÷ 2
= 2 u
The amount that Ethan has at first in Case 1 and Case 2 is the same.
3 u - 16 = 2 u + 12
3 u - 2 u = 12 + 16
1 u = 28
Amount that Ethan has
= 2 u + 12
= 2 x 28 + 12
= 56 + 12
= $68
(b)
Amount that Xylia has
= 1 u + 16
= 28 + 16
= $44
Answer(s): (a) $68; (b) $44