Henry and Jean has some money each. If Jean gives Henry $11, he will have 5 times as much money as her. If Henry gives Jean $12, he will have the same amount of money as her. How much money does each person have respectively?
- Henry?
- Jean?
| |
Case 1 |
Case 2 |
| |
Henry |
Jean |
Henry |
Jean |
| Before |
5 u - 11 |
1 u + 11 |
3 u + 12 |
3 u - 12 |
| Change |
+ 11 |
- 11 |
- 12 |
+ 12 |
| After |
5 u |
1 u |
3 u |
3 u |
(a)
If Jean gives Henry some money or Henry gives Jean some money, the total amount of money remains the same.
Total amount that Henry and Jean have in the end for both cases
= 5 u + 1 u
= 6 u
Amount that Henry and Jean each has in the end in Case 2
= 6 u ÷ 2
= 3 u
The amount that Henry has at first in Case 1 and Case 2 is the same.
5 u - 11 = 3 u + 12
5 u - 3 u = 12 + 11
1 u = 23
Amount that Henry has
= 3 u + 12
= 3 x 23 + 12
= 69 + 12
= $81
(b)
Amount that Jean has
= 1 u + 11
= 23 + 11
= $34
Answer(s): (a) $81; (b) $34
