If Mary gives Tom $28, the amount of money she has will be 40% of his. If Tom gives Mary $2, he will have the same amount of money as her. How much money did each of them have?
(a) Tom
(b) Mary
|
Case 1 |
Case 2 |
|
Tom |
Mary |
Tom |
Mary |
Before |
5 u - 28 |
2 u + 28 |
3.5 u + 2 |
3.5 u - 2 |
Change |
+ 28 |
- 28 |
- 2 |
+ 2 |
After |
5 u |
2 u |
3.5 u |
3.5 u |
(a)
40% =
40100 =
25 In Case 1, when Mary gives to Tom, there is an internal transfer of money from Mary to Tom. The total amount that both have remains the same.
In Case 2, when Tom gives to Mary, there is an internal transfer of money from Tom to Mary. 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 Mary and Tom have
= 5 u + 2 u
= 7 u
Amount that Mary and Tom each has in the end for Case 2
= 7 u ÷ 2
= 3.5 u
Amount that Tom has at first is the same in Case 1 and Case 2.
5 u - 28 = 3.5 u + 2
5 u - 3.5 u = 2 + 28
1.5 u = 30
1 u = 30 ÷ 1.5 = 20
Amount that Tom has
= 5 u - 28
= 5 x 20 - 28
= 100 - 28
= $72
(b)
Amount that Mary has
= 2 u + 28
= 2 x 20 + 28
= 40 + 28
= $68
Answer(s): (a) $72; (b) $68