If Roshel gives Rael $16, the amount of money she has will be 30% of his. If Rael gives Roshel $124, he will have the same amount of money as her. How much money did each of them have?
(a) Rael
(b) Roshel
|
Case 1 |
Case 2 |
|
Rael |
Roshel |
Rael |
Roshel |
Before |
10 u - 16 |
3 u + 16 |
6.5 u + 124 |
6.5 u - 124 |
Change |
+ 16 |
- 16 |
- 124 |
+ 124 |
After |
10 u |
3 u |
6.5 u |
6.5 u |
(a)
30% =
30100 =
310 In Case 1, when Roshel gives to Rael, there is an internal transfer of money from Roshel to Rael. The total amount that both have remains the same.
In Case 2, when Rael gives to Roshel, there is an internal transfer of money from Rael 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 Rael have
= 10 u + 3 u
= 13 u
Amount that Roshel and Rael each has in the end for Case 2
= 13 u ÷ 2
= 6.5 u
Amount that Rael has at first is the same in Case 1 and Case 2.
10 u - 16 = 6.5 u + 124
10 u - 6.5 u = 124 + 16
3.5 u = 140
1 u = 140 ÷ 3.5 = 40
Amount that Rael has
= 10 u - 16
= 10 x 40 - 16
= 400 - 16
= $384
(b)
Amount that Roshel has
= 3 u + 16
= 3 x 40 + 16
= 120 + 16
= $136
Answer(s): (a) $384; (b) $136