If Usha gives George $17, the amount of money she has will be 40% of his. If George gives Usha $34, he will have the same amount of money as her. How much money did each of them have?
(a) George
(b) Usha
|
Case 1 |
Case 2 |
|
George |
Usha |
George |
Usha |
Before |
5 u - 17 |
2 u + 17 |
3.5 u + 34 |
3.5 u - 34 |
Change |
+ 17 |
- 17 |
- 34 |
+ 34 |
After |
5 u |
2 u |
3.5 u |
3.5 u |
(a)
40% =
40100 =
25 In Case 1, when Usha gives to George, there is an internal transfer of money from Usha to George. The total amount that both have remains the same.
In Case 2, when George gives to Usha, there is an internal transfer of money from George to Usha. 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 Usha and George have
= 5 u + 2 u
= 7 u
Amount that Usha and George each has in the end for Case 2
= 7 u ÷ 2
= 3.5 u
Amount that George has at first is the same in Case 1 and Case 2.
5 u - 17 = 3.5 u + 34
5 u - 3.5 u = 34 + 17
1.5 u = 51
1 u = 51 ÷ 1.5 = 34
Amount that George has
= 5 u - 17
= 5 x 34 - 17
= 170 - 17
= $153
(b)
Amount that Usha has
= 2 u + 17
= 2 x 34 + 17
= 68 + 17
= $85
Answer(s): (a) $153; (b) $85