If Julie gives Dylan $31, the amount of money she has will be 10% of his. If Dylan gives Julie $158, he will have the same amount of money as her. How much money did each of them have?
(a) Dylan
(b) Julie
|
Case 1 |
Case 2 |
|
Dylan |
Julie |
Dylan |
Julie |
Before |
10 u - 31 |
1 u + 31 |
5.5 u + 158 |
5.5 u - 158 |
Change |
+ 31 |
- 31 |
- 158 |
+ 158 |
After |
10 u |
1 u |
5.5 u |
5.5 u |
(a)
10% =
10100 =
110 In Case 1, when Julie gives to Dylan, there is an internal transfer of money from Julie to Dylan. The total amount that both have remains the same.
In Case 2, when Dylan gives to Julie, there is an internal transfer of money from Dylan to Julie. 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 Julie and Dylan have
= 10 u + 1 u
= 11 u
Amount that Julie and Dylan each has in the end for Case 2
= 11 u ÷ 2
= 5.5 u
Amount that Dylan has at first is the same in Case 1 and Case 2.
10 u - 31 = 5.5 u + 158
10 u - 5.5 u = 158 + 31
4.5 u = 189
1 u = 189 ÷ 4.5 = 42
Amount that Dylan has
= 10 u - 31
= 10 x 42 - 31
= 420 - 31
= $389
(b)
Amount that Julie has
= 1 u + 31
= 1 x 42 + 31
= 42 + 31
= $73
Answer(s): (a) $389; (b) $73