Eric and Esther has some money each. If Esther gives Eric $20, he will have 3 times as much money as her. If Eric gives Esther $19, he will have the same amount of money as her. How much money does each person have respectively?
- Eric?
- Esther?
| |
Case 1 |
Case 2 |
| |
Eric |
Esther |
Eric |
Esther |
| Before |
3 u - 20 |
1 u + 20 |
2 u + 19 |
2 u - 19 |
| Change |
+ 20 |
- 20 |
- 19 |
+ 19 |
| After |
3 u |
1 u |
2 u |
2 u |
(a)
If Esther gives Eric some money or Eric gives Esther some money, the total amount of money remains the same.
Total amount that Eric and Esther have in the end for both cases
= 3 u + 1 u
= 4 u
Amount that Eric and Esther each has in the end in Case 2
= 4 u ÷ 2
= 2 u
The amount that Eric has at first in Case 1 and Case 2 is the same.
3 u - 20 = 2 u + 19
3 u - 2 u = 19 + 20
1 u = 39
Amount that Eric has
= 2 u + 19
= 2 x 39 + 19
= 78 + 19
= $97
(b)
Amount that Esther has
= 1 u + 20
= 39 + 20
= $59
Answer(s): (a) $97; (b) $59
