If Diana gives Seth $26, the amount of money she has will be 30% of his. If Seth gives Diana $51, he will have the same amount of money as her. How much money did each of them have?
(a) Seth
(b) Diana
|
Case 1 |
Case 2 |
|
Seth |
Diana |
Seth |
Diana |
Before |
10 u - 26 |
3 u + 26 |
6.5 u + 51 |
6.5 u - 51 |
Change |
+ 26 |
- 26 |
- 51 |
+ 51 |
After |
10 u |
3 u |
6.5 u |
6.5 u |
(a)
30% =
30100 =
310 In Case 1, when Diana gives to Seth, there is an internal transfer of money from Diana to Seth. The total amount that both have remains the same.
In Case 2, when Seth gives to Diana, there is an internal transfer of money from Seth to Diana. 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 Diana and Seth have
= 10 u + 3 u
= 13 u
Amount that Diana and Seth each has in the end for Case 2
= 13 u ÷ 2
= 6.5 u
Amount that Seth has at first is the same in Case 1 and Case 2.
10 u - 26 = 6.5 u + 51
10 u - 6.5 u = 51 + 26
3.5 u = 77
1 u = 77 ÷ 3.5 = 22
Amount that Seth has
= 10 u - 26
= 10 x 22 - 26
= 220 - 26
= $194
(b)
Amount that Diana has
= 3 u + 26
= 3 x 22 + 26
= 66 + 26
= $92
Answer(s): (a) $194; (b) $92