If Irene gives David $23, the amount of money she has will be 40% of his. If David gives Irene $46, he will have the same amount of money as her. How much money did each of them have?
(a) David
(b) Irene
|
Case 1 |
Case 2 |
|
David |
Irene |
David |
Irene |
Before |
5 u - 23 |
2 u + 23 |
3.5 u + 46 |
3.5 u - 46 |
Change |
+ 23 |
- 23 |
- 46 |
+ 46 |
After |
5 u |
2 u |
3.5 u |
3.5 u |
(a)
40% =
40100 =
25 In Case 1, when Irene gives to David, there is an internal transfer of money from Irene to David. The total amount that both have remains the same.
In Case 2, when David gives to Irene, there is an internal transfer of money from David to Irene. 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 Irene and David have
= 5 u + 2 u
= 7 u
Amount that Irene and David each has in the end for Case 2
= 7 u ÷ 2
= 3.5 u
Amount that David has at first is the same in Case 1 and Case 2.
5 u - 23 = 3.5 u + 46
5 u - 3.5 u = 46 + 23
1.5 u = 69
1 u = 69 ÷ 1.5 = 46
Amount that David has
= 5 u - 23
= 5 x 46 - 23
= 230 - 23
= $207
(b)
Amount that Irene has
= 2 u + 23
= 2 x 46 + 23
= 92 + 23
= $115
Answer(s): (a) $207; (b) $115