If Dana gives Fabian $39, the amount of money she has will be 30% of his. If Fabian gives Dana $101, he will have the same amount of money as her. How much money did each of them have?
(a) Fabian
(b) Dana
|
Case 1 |
Case 2 |
|
Fabian |
Dana |
Fabian |
Dana |
Before |
10 u - 39 |
3 u + 39 |
6.5 u + 101 |
6.5 u - 101 |
Change |
+ 39 |
- 39 |
- 101 |
+ 101 |
After |
10 u |
3 u |
6.5 u |
6.5 u |
(a)
30% =
30100 =
310 In Case 1, when Dana gives to Fabian, there is an internal transfer of money from Dana to Fabian. The total amount that both have remains the same.
In Case 2, when Fabian gives to Dana, there is an internal transfer of money from Fabian to Dana. 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 Dana and Fabian have
= 10 u + 3 u
= 13 u
Amount that Dana and Fabian each has in the end for Case 2
= 13 u ÷ 2
= 6.5 u
Amount that Fabian has at first is the same in Case 1 and Case 2.
10 u - 39 = 6.5 u + 101
10 u - 6.5 u = 101 + 39
3.5 u = 140
1 u = 140 ÷ 3.5 = 40
Amount that Fabian has
= 10 u - 39
= 10 x 40 - 39
= 400 - 39
= $361
(b)
Amount that Dana has
= 3 u + 39
= 3 x 40 + 39
= 120 + 39
= $159
Answer(s): (a) $361; (b) $159