If Jean gives Henry $15, the amount of money she has will be 40% of his. If Henry gives Jean $30, he will have the same amount of money as her. How much money did each of them have?
(a) Henry
(b) Jean
|
Case 1 |
Case 2 |
|
Henry |
Jean |
Henry |
Jean |
Before |
5 u - 15 |
2 u + 15 |
3.5 u + 30 |
3.5 u - 30 |
Change |
+ 15 |
- 15 |
- 30 |
+ 30 |
After |
5 u |
2 u |
3.5 u |
3.5 u |
(a)
40% =
40100 =
25 In Case 1, when Jean gives to Henry, there is an internal transfer of money from Jean to Henry. The total amount that both have remains the same.
In Case 2, when Henry gives to Jean, there is an internal transfer of money from Henry to Jean. The total amount that both have remains the same.
The total amount that both have in Case 1 and Case 2 are the same.
Total amount that Jean and Henry have
= 5 u + 2 u
= 7 u
Amount that Jean and Henry each has in the end for Case 2
= 7 u ÷ 2
= 3.5 u
Amount that Henry has at first is the same in Case 1 and Case 2.
5 u - 15 = 3.5 u + 30
5 u - 3.5 u = 30 + 15
1.5 u = 45
1 u = 45 ÷ 1.5 = 30
Amount that Henry has
= 5 u - 15
= 5 x 30 - 15
= 150 - 15
= $135
(b)
Amount that Jean has
= 2 u + 15
= 2 x 30 + 15
= 60 + 15
= $75
Answer(s): (a) $135; (b) $75