Charlie and Irene has some money each. If Irene gives Charlie $18, he will have 3 times as much money as her. If Charlie gives Irene $11, he will have the same amount of money as her. How much money does each person have respectively?
- Charlie?
- Irene?
| |
Case 1 |
Case 2 |
| |
Charlie |
Irene |
Charlie |
Irene |
| Before |
3 u - 18 |
1 u + 18 |
2 u + 11 |
2 u - 11 |
| Change |
+ 18 |
- 18 |
- 11 |
+ 11 |
| After |
3 u |
1 u |
2 u |
2 u |
(a)
If Irene gives Charlie some money or Charlie gives Irene some money, the total amount of money remains the same.
Total amount that Charlie and Irene have in the end for both cases
= 3 u + 1 u
= 4 u
Amount that Charlie and Irene each has in the end in Case 2
= 4 u ÷ 2
= 2 u
The amount that Charlie has at first in Case 1 and Case 2 is the same.
3 u - 18 = 2 u + 11
3 u - 2 u = 11 + 18
1 u = 29
Amount that Charlie has
= 2 u + 11
= 2 x 29 + 11
= 58 + 11
= $69
(b)
Amount that Irene has
= 1 u + 18
= 29 + 18
= $47
Answer(s): (a) $69; (b) $47
