Ethan and Zoe has some money each. If Zoe gives Ethan $19, he will have 5 times as much money as her. If Ethan gives Zoe $12, he will have the same amount of money as her. How much money does each person have respectively?
- Ethan?
- Zoe?
|
Case 1 |
Case 2 |
|
Ethan |
Zoe |
Ethan |
Zoe |
Before |
5 u - 19 |
1 u + 19 |
3 u + 12 |
3 u - 12 |
Change |
+ 19 |
- 19 |
- 12 |
+ 12 |
After |
5 u |
1 u |
3 u |
3 u |
(a)
If Zoe gives Ethan some money or Ethan gives Zoe some money, the total amount of money remains the same.
Total amount that Ethan and Zoe have in the end for both cases
= 5 u + 1 u
= 6 u
Amount that Ethan and Zoe each has in the end in Case 2
= 6 u ÷ 2
= 3 u
The amount that Ethan has at first in Case 1 and Case 2 is the same.
5 u - 19 = 3 u + 12
5 u - 3 u = 12 + 19
1 u = 31
Amount that Ethan has
= 3 u + 12
= 3 x 31 + 12
= 93 + 12
= $105
(b)
Amount that Zoe has
= 1 u + 19
= 31 + 19
= $50
Answer(s): (a) $105; (b) $50