If Roshel gives George $18, the amount of money she has will be 30% of his. If George gives Roshel $157, he will have the same amount of money as her. How much money did each of them have?
(a) George
(b) Roshel
|
Case 1 |
Case 2 |
|
George |
Roshel |
George |
Roshel |
Before |
10 u - 18 |
3 u + 18 |
6.5 u + 157 |
6.5 u - 157 |
Change |
+ 18 |
- 18 |
- 157 |
+ 157 |
After |
10 u |
3 u |
6.5 u |
6.5 u |
(a)
30% =
30100 =
310 In Case 1, when Roshel gives to George, there is an internal transfer of money from Roshel to George. The total amount that both have remains the same.
In Case 2, when George gives to Roshel, there is an internal transfer of money from George to Roshel. 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 Roshel and George have
= 10 u + 3 u
= 13 u
Amount that Roshel and George each has in the end for Case 2
= 13 u ÷ 2
= 6.5 u
Amount that George has at first is the same in Case 1 and Case 2.
10 u - 18 = 6.5 u + 157
10 u - 6.5 u = 157 + 18
3.5 u = 175
1 u = 175 ÷ 3.5 = 50
Amount that George has
= 10 u - 18
= 10 x 50 - 18
= 500 - 18
= $482
(b)
Amount that Roshel has
= 3 u + 18
= 3 x 50 + 18
= 150 + 18
= $168
Answer(s): (a) $482; (b) $168