Henry and Linda has some money each. If Linda gives Henry $17, he will have 7 times as much money as her. If Henry gives Linda $13, he will have the same amount of money as her. How much money does each person have respectively?
- Henry?
- Linda?
| |
Case 1 |
Case 2 |
| |
Henry |
Linda |
Henry |
Linda |
| Before |
7 u - 17 |
1 u + 17 |
4 u + 13 |
4 u - 13 |
| Change |
+ 17 |
- 17 |
- 13 |
+ 13 |
| After |
7 u |
1 u |
4 u |
4 u |
(a)
If Linda gives Henry some money or Henry gives Linda some money, the total amount of money remains the same.
Total amount that Henry and Linda have in the end for both cases
= 7 u + 1 u
= 8 u
Amount that Henry and Linda each has in the end in Case 2
= 8 u ÷ 2
= 4 u
The amount that Henry has at first in Case 1 and Case 2 is the same.
7 u - 17 = 4 u + 13
7 u - 4 u = 13 + 17
1 u = 30
Amount that Henry has
= 4 u + 13
= 4 x 30 + 13
= 120 + 13
= $133
(b)
Amount that Linda has
= 1 u + 17
= 30 + 17
= $47
Answer(s): (a) $133; (b) $47
