Harry and Irene has some money each. If Irene gives Harry $11, he will have 3 times as much money as her. If Harry gives Irene $13, he will have the same amount of money as her. How much money does each person have respectively?
- Harry?
- Irene?
| |
Case 1 |
Case 2 |
| |
Harry |
Irene |
Harry |
Irene |
| Before |
3 u - 11 |
1 u + 11 |
2 u + 13 |
2 u - 13 |
| Change |
+ 11 |
- 11 |
- 13 |
+ 13 |
| After |
3 u |
1 u |
2 u |
2 u |
(a)
If Irene gives Harry some money or Harry gives Irene some money, the total amount of money remains the same.
Total amount that Harry and Irene have in the end for both cases
= 3 u + 1 u
= 4 u
Amount that Harry and Irene each has in the end in Case 2
= 4 u ÷ 2
= 2 u
The amount that Harry has at first in Case 1 and Case 2 is the same.
3 u - 11 = 2 u + 13
3 u - 2 u = 13 + 11
1 u = 24
Amount that Harry has
= 2 u + 13
= 2 x 24 + 13
= 48 + 13
= $61
(b)
Amount that Irene has
= 1 u + 11
= 24 + 11
= $35
Answer(s): (a) $61; (b) $35
