If Mary gives Tommy $40, the amount of money she has will be 10% of his. If Tommy gives Mary $50, he will have the same amount of money as her. How much money did each of them have?
(a) Tommy
(b) Mary
|
Case 1 |
Case 2 |
|
Tommy |
Mary |
Tommy |
Mary |
Before |
10 u - 40 |
1 u + 40 |
5.5 u + 50 |
5.5 u - 50 |
Change |
+ 40 |
- 40 |
- 50 |
+ 50 |
After |
10 u |
1 u |
5.5 u |
5.5 u |
(a)
10% =
10100 =
110 In Case 1, when Mary gives to Tommy, there is an internal transfer of money from Mary to Tommy. The total amount that both have remains the same.
In Case 2, when Tommy gives to Mary, there is an internal transfer of money from Tommy 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 Tommy have
= 10 u + 1 u
= 11 u
Amount that Mary and Tommy each has in the end for Case 2
= 11 u ÷ 2
= 5.5 u
Amount that Tommy has at first is the same in Case 1 and Case 2.
10 u - 40 = 5.5 u + 50
10 u - 5.5 u = 50 + 40
4.5 u = 90
1 u = 90 ÷ 4.5 = 20
Amount that Tommy has
= 10 u - 40
= 10 x 20 - 40
= 200 - 40
= $160
(b)
Amount that Mary has
= 1 u + 40
= 1 x 20 + 40
= 20 + 40
= $60
Answer(s): (a) $160; (b) $60