If Ivory gives Zane $23, the amount of money she has will be 25% of his. If Zane gives Ivory $43, he will have the same amount of money as her. How much money did each of them have?
(a) Zane
(b) Ivory
|
Case 1 |
Case 2 |
|
Zane |
Ivory |
Zane |
Ivory |
Before |
4 u - 23 |
1 u + 23 |
2.5 u + 43 |
2.5 u - 43 |
Change |
+ 23 |
- 23 |
- 43 |
+ 43 |
After |
4 u |
1 u |
2.5 u |
2.5 u |
(a)
25% =
25100 =
14 In Case 1, when Ivory gives to Zane, there is an internal transfer of money from Ivory to Zane. The total amount that both have remains the same.
In Case 2, when Zane gives to Ivory, there is an internal transfer of money from Zane to Ivory. 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 Ivory and Zane have
= 4 u + 1 u
= 5 u
Amount that Ivory and Zane each has in the end for Case 2
= 5 u ÷ 2
= 2.5 u
Amount that Zane has at first is the same in Case 1 and Case 2.
4 u - 23 = 2.5 u + 43
4 u - 2.5 u = 43 + 23
1.5 u = 66
1 u = 66 ÷ 1.5 = 44
Amount that Zane has
= 4 u - 23
= 4 x 44 - 23
= 176 - 23
= $153
(b)
Amount that Ivory has
= 1 u + 23
= 1 x 44 + 23
= 44 + 23
= $67
Answer(s): (a) $153; (b) $67