If Eva gives Warren $31, the amount of money she has will be 10% of his. If Warren gives Eva $122, he will have the same amount of money as her. How much money did each of them have?
(a) Warren
(b) Eva
|
Case 1 |
Case 2 |
|
Warren |
Eva |
Warren |
Eva |
Before |
10 u - 31 |
1 u + 31 |
5.5 u + 122 |
5.5 u - 122 |
Change |
+ 31 |
- 31 |
- 122 |
+ 122 |
After |
10 u |
1 u |
5.5 u |
5.5 u |
(a)
10% =
10100 =
110 In Case 1, when Eva gives to Warren, there is an internal transfer of money from Eva to Warren. The total amount that both have remains the same.
In Case 2, when Warren gives to Eva, there is an internal transfer of money from Warren to Eva. 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 Eva and Warren have
= 10 u + 1 u
= 11 u
Amount that Eva and Warren each has in the end for Case 2
= 11 u ÷ 2
= 5.5 u
Amount that Warren has at first is the same in Case 1 and Case 2.
10 u - 31 = 5.5 u + 122
10 u - 5.5 u = 122 + 31
4.5 u = 153
1 u = 153 ÷ 4.5 = 34
Amount that Warren has
= 10 u - 31
= 10 x 34 - 31
= 340 - 31
= $309
(b)
Amount that Eva has
= 1 u + 31
= 1 x 34 + 31
= 34 + 31
= $65
Answer(s): (a) $309; (b) $65