If Dana gives Ahmad $23, the amount of money she has will be 10% of his. If Ahmad gives Dana $85, he will have the same amount of money as her. How much money did each of them have?
(a) Ahmad
(b) Dana
|
Case 1 |
Case 2 |
|
Ahmad |
Dana |
Ahmad |
Dana |
Before |
10 u - 23 |
1 u + 23 |
5.5 u + 85 |
5.5 u - 85 |
Change |
+ 23 |
- 23 |
- 85 |
+ 85 |
After |
10 u |
1 u |
5.5 u |
5.5 u |
(a)
10% =
10100 =
110 In Case 1, when Dana gives to Ahmad, there is an internal transfer of money from Dana to Ahmad. The total amount that both have remains the same.
In Case 2, when Ahmad gives to Dana, there is an internal transfer of money from Ahmad to Dana. 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 Dana and Ahmad have
= 10 u + 1 u
= 11 u
Amount that Dana and Ahmad each has in the end for Case 2
= 11 u ÷ 2
= 5.5 u
Amount that Ahmad has at first is the same in Case 1 and Case 2.
10 u - 23 = 5.5 u + 85
10 u - 5.5 u = 85 + 23
4.5 u = 108
1 u = 108 ÷ 4.5 = 24
Amount that Ahmad has
= 10 u - 23
= 10 x 24 - 23
= 240 - 23
= $217
(b)
Amount that Dana has
= 1 u + 23
= 1 x 24 + 23
= 24 + 23
= $47
Answer(s): (a) $217; (b) $47