If Julie gives Daniel $14, the amount of money she has will be 75% of his. If Daniel gives Julie $1, he will have the same amount of money as her. How much money did each of them have?
(a) Daniel
(b) Julie
|
Case 1 |
Case 2 |
|
Daniel |
Julie |
Daniel |
Julie |
Before |
4 u - 14 |
3 u + 14 |
3.5 u + 1 |
3.5 u - 1 |
Change |
+ 14 |
- 14 |
- 1 |
+ 1 |
After |
4 u |
3 u |
3.5 u |
3.5 u |
(a)
75% =
75100 =
34 In Case 1, when Julie gives to Daniel, there is an internal transfer of money from Julie to Daniel. The total amount that both have remains the same.
In Case 2, when Daniel gives to Julie, there is an internal transfer of money from Daniel 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 Daniel have
= 4 u + 3 u
= 7 u
Amount that Julie and Daniel each has in the end for Case 2
= 7 u ÷ 2
= 3.5 u
Amount that Daniel has at first is the same in Case 1 and Case 2.
4 u - 14 = 3.5 u + 1
4 u - 3.5 u = 1 + 14
0.5 u = 15
1 u = 15 ÷ 0.5 = 30
Amount that Daniel has
= 4 u - 14
= 4 x 30 - 14
= 120 - 14
= $106
(b)
Amount that Julie has
= 3 u + 14
= 3 x 30 + 14
= 90 + 14
= $104
Answer(s): (a) $106; (b) $104