If Zoe gives Tom $38, the amount of money she has will be 25% of his. If Tom gives Zoe $28, he will have the same amount of money as her. How much money did each of them have?
(a) Tom
(b) Zoe
|
Case 1 |
Case 2 |
|
Tom |
Zoe |
Tom |
Zoe |
Before |
4 u - 38 |
1 u + 38 |
2.5 u + 28 |
2.5 u - 28 |
Change |
+ 38 |
- 38 |
- 28 |
+ 28 |
After |
4 u |
1 u |
2.5 u |
2.5 u |
(a)
25% =
25100 =
14 In Case 1, when Zoe gives to Tom, there is an internal transfer of money from Zoe to Tom. The total amount that both have remains the same.
In Case 2, when Tom gives to Zoe, there is an internal transfer of money from Tom to Zoe. 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 Zoe and Tom have
= 4 u + 1 u
= 5 u
Amount that Zoe and Tom each has in the end for Case 2
= 5 u ÷ 2
= 2.5 u
Amount that Tom has at first is the same in Case 1 and Case 2.
4 u - 38 = 2.5 u + 28
4 u - 2.5 u = 28 + 38
1.5 u = 66
1 u = 66 ÷ 1.5 = 44
Amount that Tom has
= 4 u - 38
= 4 x 44 - 38
= 176 - 38
= $138
(b)
Amount that Zoe has
= 1 u + 38
= 1 x 44 + 38
= 44 + 38
= $82
Answer(s): (a) $138; (b) $82