Perry and Irene has some money each. If Irene gives Perry $15, he will have 3 times as much money as her. If Perry gives Irene $14, he will have the same amount of money as her. How much money does each person have respectively?
- Perry?
- Irene?
| |
Case 1 |
Case 2 |
| |
Perry |
Irene |
Perry |
Irene |
| Before |
3 u - 15 |
1 u + 15 |
2 u + 14 |
2 u - 14 |
| Change |
+ 15 |
- 15 |
- 14 |
+ 14 |
| After |
3 u |
1 u |
2 u |
2 u |
(a)
If Irene gives Perry some money or Perry gives Irene some money, the total amount of money remains the same.
Total amount that Perry and Irene have in the end for both cases
= 3 u + 1 u
= 4 u
Amount that Perry and Irene each has in the end in Case 2
= 4 u ÷ 2
= 2 u
The amount that Perry has at first in Case 1 and Case 2 is the same.
3 u - 15 = 2 u + 14
3 u - 2 u = 14 + 15
1 u = 29
Amount that Perry has
= 2 u + 14
= 2 x 29 + 14
= 58 + 14
= $72
(b)
Amount that Irene has
= 1 u + 15
= 29 + 15
= $44
Answer(s): (a) $72; (b) $44
