Henry and Elyse has some money each. If Elyse gives Henry $18, he will have 3 times as much money as her. If Henry gives Elyse $14, he will have the same amount of money as her. How much money does each person have respectively?
- Henry?
- Elyse?
|
Case 1 |
Case 2 |
|
Henry |
Elyse |
Henry |
Elyse |
Before |
3 u - 18 |
1 u + 18 |
2 u + 14 |
2 u - 14 |
Change |
+ 18 |
- 18 |
- 14 |
+ 14 |
After |
3 u |
1 u |
2 u |
2 u |
(a)
If Elyse gives Henry some money or Henry gives Elyse some money, the total amount of money remains the same.
Total amount that Henry and Elyse have in the end for both cases
= 3 u + 1 u
= 4 u
Amount that Henry and Elyse 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 - 18 = 2 u + 14
3 u - 2 u = 14 + 18
1 u = 32
Amount that Henry has
= 2 u + 14
= 2 x 32 + 14
= 64 + 14
= $78
(b)
Amount that Elyse has
= 1 u + 18
= 32 + 18
= $50
Answer(s): (a) $78; (b) $50