If Zoe gives Albert $28, the amount of money she has will be 10% of his. If Albert gives Zoe $161, he will have the same amount of money as her. How much money did each of them have?
(a) Albert
(b) Zoe
|
Case 1 |
Case 2 |
|
Albert |
Zoe |
Albert |
Zoe |
Before |
10 u - 28 |
1 u + 28 |
5.5 u + 161 |
5.5 u - 161 |
Change |
+ 28 |
- 28 |
- 161 |
+ 161 |
After |
10 u |
1 u |
5.5 u |
5.5 u |
(a)
10% =
10100 =
110 In Case 1, when Zoe gives to Albert, there is an internal transfer of money from Zoe to Albert. The total amount that both have remains the same.
In Case 2, when Albert gives to Zoe, there is an internal transfer of money from Albert to Zoe. 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 Zoe and Albert have
= 10 u + 1 u
= 11 u
Amount that Zoe and Albert each has in the end for Case 2
= 11 u ÷ 2
= 5.5 u
Amount that Albert has at first is the same in Case 1 and Case 2.
10 u - 28 = 5.5 u + 161
10 u - 5.5 u = 161 + 28
4.5 u = 189
1 u = 189 ÷ 4.5 = 42
Amount that Albert has
= 10 u - 28
= 10 x 42 - 28
= 420 - 28
= $392
(b)
Amount that Zoe has
= 1 u + 28
= 1 x 42 + 28
= 42 + 28
= $70
Answer(s): (a) $392; (b) $70