If Gabby gives Henry $23, the amount of money she has will be 10% of his. If Henry gives Gabby $103, he will have the same amount of money as her. How much money did each of them have?
(a) Henry
(b) Gabby
|
Case 1 |
Case 2 |
|
Henry |
Gabby |
Henry |
Gabby |
Before |
10 u - 23 |
1 u + 23 |
5.5 u + 103 |
5.5 u - 103 |
Change |
+ 23 |
- 23 |
- 103 |
+ 103 |
After |
10 u |
1 u |
5.5 u |
5.5 u |
(a)
10% =
10100 =
110 In Case 1, when Gabby gives to Henry, there is an internal transfer of money from Gabby to Henry. The total amount that both have remains the same.
In Case 2, when Henry gives to Gabby, there is an internal transfer of money from Henry to Gabby. 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 Gabby and Henry have
= 10 u + 1 u
= 11 u
Amount that Gabby and Henry each has in the end for Case 2
= 11 u ÷ 2
= 5.5 u
Amount that Henry has at first is the same in Case 1 and Case 2.
10 u - 23 = 5.5 u + 103
10 u - 5.5 u = 103 + 23
4.5 u = 126
1 u = 126 ÷ 4.5 = 28
Amount that Henry has
= 10 u - 23
= 10 x 28 - 23
= 280 - 23
= $257
(b)
Amount that Gabby has
= 1 u + 23
= 1 x 28 + 23
= 28 + 23
= $51
Answer(s): (a) $257; (b) $51