Henry and Dana has some money each. If Dana gives Henry $12, he will have 3 times as much money as her. If Henry gives Dana $19, he will have the same amount of money as her. How much money does each person have respectively?
- Henry?
- Dana?
| |
Case 1 |
Case 2 |
| |
Henry |
Dana |
Henry |
Dana |
| Before |
3 u - 12 |
1 u + 12 |
2 u + 19 |
2 u - 19 |
| Change |
+ 12 |
- 12 |
- 19 |
+ 19 |
| After |
3 u |
1 u |
2 u |
2 u |
(a)
If Dana gives Henry some money or Henry gives Dana some money, the total amount of money remains the same.
Total amount that Henry and Dana have in the end for both cases
= 3 u + 1 u
= 4 u
Amount that Henry and Dana each has in the end in Case 2
= 4 u ÷ 2
= 2 u
The amount that Henry has at first in Case 1 and Case 2 is the same.
3 u - 12 = 2 u + 19
3 u - 2 u = 19 + 12
1 u = 31
Amount that Henry has
= 2 u + 19
= 2 x 31 + 19
= 62 + 19
= $81
(b)
Amount that Dana has
= 1 u + 12
= 31 + 12
= $43
Answer(s): (a) $81; (b) $43
