If Emma gives Harry $33, the amount of money she has will be 30% of his. If Harry gives Emma $142, he will have the same amount of money as her. How much money did each of them have?
(a) Harry
(b) Emma
|
Case 1 |
Case 2 |
|
Harry |
Emma |
Harry |
Emma |
Before |
10 u - 33 |
3 u + 33 |
6.5 u + 142 |
6.5 u - 142 |
Change |
+ 33 |
- 33 |
- 142 |
+ 142 |
After |
10 u |
3 u |
6.5 u |
6.5 u |
(a)
30% =
30100 =
310 In Case 1, when Emma gives to Harry, there is an internal transfer of money from Emma to Harry. The total amount that both have remains the same.
In Case 2, when Harry gives to Emma, there is an internal transfer of money from Harry to Emma. 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 Emma and Harry have
= 10 u + 3 u
= 13 u
Amount that Emma and Harry each has in the end for Case 2
= 13 u ÷ 2
= 6.5 u
Amount that Harry has at first is the same in Case 1 and Case 2.
10 u - 33 = 6.5 u + 142
10 u - 6.5 u = 142 + 33
3.5 u = 175
1 u = 175 ÷ 3.5 = 50
Amount that Harry has
= 10 u - 33
= 10 x 50 - 33
= 500 - 33
= $467
(b)
Amount that Emma has
= 3 u + 33
= 3 x 50 + 33
= 150 + 33
= $183
Answer(s): (a) $467; (b) $183