If Diana gives Sean $32, the amount of money she has will be 10% of his. If Sean gives Diana $121, he will have the same amount of money as her. How much money did each of them have?
(a) Sean
(b) Diana
|
Case 1 |
Case 2 |
|
Sean |
Diana |
Sean |
Diana |
Before |
10 u - 32 |
1 u + 32 |
5.5 u + 121 |
5.5 u - 121 |
Change |
+ 32 |
- 32 |
- 121 |
+ 121 |
After |
10 u |
1 u |
5.5 u |
5.5 u |
(a)
10% =
10100 =
110 In Case 1, when Diana gives to Sean, there is an internal transfer of money from Diana to Sean. The total amount that both have remains the same.
In Case 2, when Sean gives to Diana, there is an internal transfer of money from Sean 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 Sean have
= 10 u + 1 u
= 11 u
Amount that Diana and Sean each has in the end for Case 2
= 11 u ÷ 2
= 5.5 u
Amount that Sean has at first is the same in Case 1 and Case 2.
10 u - 32 = 5.5 u + 121
10 u - 5.5 u = 121 + 32
4.5 u = 153
1 u = 153 ÷ 4.5 = 34
Amount that Sean has
= 10 u - 32
= 10 x 34 - 32
= 340 - 32
= $308
(b)
Amount that Diana has
= 1 u + 32
= 1 x 34 + 32
= 34 + 32
= $66
Answer(s): (a) $308; (b) $66