If Roshel gives Asher $24, the amount of money she has will be 30% of his. If Asher gives Roshel $88, he will have the same amount of money as her. How much money did each of them have?
(a) Asher
(b) Roshel
|
Case 1 |
Case 2 |
|
Asher |
Roshel |
Asher |
Roshel |
Before |
10 u - 24 |
3 u + 24 |
6.5 u + 88 |
6.5 u - 88 |
Change |
+ 24 |
- 24 |
- 88 |
+ 88 |
After |
10 u |
3 u |
6.5 u |
6.5 u |
(a)
30% =
30100 =
310 In Case 1, when Roshel gives to Asher, there is an internal transfer of money from Roshel to Asher. The total amount that both have remains the same.
In Case 2, when Asher gives to Roshel, there is an internal transfer of money from Asher 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 Asher have
= 10 u + 3 u
= 13 u
Amount that Roshel and Asher each has in the end for Case 2
= 13 u ÷ 2
= 6.5 u
Amount that Asher has at first is the same in Case 1 and Case 2.
10 u - 24 = 6.5 u + 88
10 u - 6.5 u = 88 + 24
3.5 u = 112
1 u = 112 ÷ 3.5 = 32
Amount that Asher has
= 10 u - 24
= 10 x 32 - 24
= 320 - 24
= $296
(b)
Amount that Roshel has
= 3 u + 24
= 3 x 32 + 24
= 96 + 24
= $120
Answer(s): (a) $296; (b) $120