Eric and Irene has some money each. If Irene gives Eric $20, he will have 5 times as much money as her. If Eric gives Irene $12, he will have the same amount of money as her. How much money does each person have respectively?
- Eric?
- Irene?
| |
Case 1 |
Case 2 |
| |
Eric |
Irene |
Eric |
Irene |
| Before |
5 u - 20 |
1 u + 20 |
3 u + 12 |
3 u - 12 |
| Change |
+ 20 |
- 20 |
- 12 |
+ 12 |
| After |
5 u |
1 u |
3 u |
3 u |
(a)
If Irene gives Eric some money or Eric gives Irene some money, the total amount of money remains the same.
Total amount that Eric and Irene have in the end for both cases
= 5 u + 1 u
= 6 u
Amount that Eric and Irene each has in the end in Case 2
= 6 u ÷ 2
= 3 u
The amount that Eric has at first in Case 1 and Case 2 is the same.
5 u - 20 = 3 u + 12
5 u - 3 u = 12 + 20
1 u = 32
Amount that Eric has
= 3 u + 12
= 3 x 32 + 12
= 96 + 12
= $108
(b)
Amount that Irene has
= 1 u + 20
= 32 + 20
= $52
Answer(s): (a) $108; (b) $52
