If Mary gives Lee $17, the amount of money she has will be 40% of his. If Lee gives Mary $19, he will have the same amount of money as her. How much money did each of them have?
(a) Lee
(b) Mary
|
Case 1 |
Case 2 |
|
Lee |
Mary |
Lee |
Mary |
Before |
5 u - 17 |
2 u + 17 |
3.5 u + 19 |
3.5 u - 19 |
Change |
+ 17 |
- 17 |
- 19 |
+ 19 |
After |
5 u |
2 u |
3.5 u |
3.5 u |
(a)
40% =
40100 =
25 In Case 1, when Mary gives to Lee, there is an internal transfer of money from Mary to Lee. The total amount that both have remains the same.
In Case 2, when Lee gives to Mary, there is an internal transfer of money from Lee 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 Lee have
= 5 u + 2 u
= 7 u
Amount that Mary and Lee each has in the end for Case 2
= 7 u ÷ 2
= 3.5 u
Amount that Lee has at first is the same in Case 1 and Case 2.
5 u - 17 = 3.5 u + 19
5 u - 3.5 u = 19 + 17
1.5 u = 36
1 u = 36 ÷ 1.5 = 24
Amount that Lee has
= 5 u - 17
= 5 x 24 - 17
= 120 - 17
= $103
(b)
Amount that Mary has
= 2 u + 17
= 2 x 24 + 17
= 48 + 17
= $65
Answer(s): (a) $103; (b) $65