If Emma gives Albert $23, the amount of money she has will be 40% of his. If Albert gives Emma $34, he will have the same amount of money as her. How much money did each of them have?
(a) Albert
(b) Emma
|
Case 1 |
Case 2 |
|
Albert |
Emma |
Albert |
Emma |
Before |
5 u - 23 |
2 u + 23 |
3.5 u + 34 |
3.5 u - 34 |
Change |
+ 23 |
- 23 |
- 34 |
+ 34 |
After |
5 u |
2 u |
3.5 u |
3.5 u |
(a)
40% =
40100 =
25 In Case 1, when Emma gives to Albert, there is an internal transfer of money from Emma to Albert. The total amount that both have remains the same.
In Case 2, when Albert gives to Emma, there is an internal transfer of money from Albert 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 Albert have
= 5 u + 2 u
= 7 u
Amount that Emma and Albert each has in the end for Case 2
= 7 u ÷ 2
= 3.5 u
Amount that Albert has at first is the same in Case 1 and Case 2.
5 u - 23 = 3.5 u + 34
5 u - 3.5 u = 34 + 23
1.5 u = 57
1 u = 57 ÷ 1.5 = 38
Amount that Albert has
= 5 u - 23
= 5 x 38 - 23
= 190 - 23
= $167
(b)
Amount that Emma has
= 2 u + 23
= 2 x 38 + 23
= 76 + 23
= $99
Answer(s): (a) $167; (b) $99