If Gabby gives Howard $35, the amount of money she has will be 10% of his. If Howard gives Gabby $145, he will have the same amount of money as her. How much money did each of them have?
(a) Howard
(b) Gabby
|
Case 1 |
Case 2 |
|
Howard |
Gabby |
Howard |
Gabby |
Before |
10 u - 35 |
1 u + 35 |
5.5 u + 145 |
5.5 u - 145 |
Change |
+ 35 |
- 35 |
- 145 |
+ 145 |
After |
10 u |
1 u |
5.5 u |
5.5 u |
(a)
10% =
10100 =
110 In Case 1, when Gabby gives to Howard, there is an internal transfer of money from Gabby to Howard. The total amount that both have remains the same.
In Case 2, when Howard gives to Gabby, there is an internal transfer of money from Howard 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 Howard have
= 10 u + 1 u
= 11 u
Amount that Gabby and Howard each has in the end for Case 2
= 11 u ÷ 2
= 5.5 u
Amount that Howard has at first is the same in Case 1 and Case 2.
10 u - 35 = 5.5 u + 145
10 u - 5.5 u = 145 + 35
4.5 u = 180
1 u = 180 ÷ 4.5 = 40
Amount that Howard has
= 10 u - 35
= 10 x 40 - 35
= 400 - 35
= $365
(b)
Amount that Gabby has
= 1 u + 35
= 1 x 40 + 35
= 40 + 35
= $75
Answer(s): (a) $365; (b) $75