If Yen gives Asher $27, the amount of money she has will be 30% of his. If Asher gives Yen $141, he will have the same amount of money as her. How much money did each of them have?
(a) Asher
(b) Yen
|
Case 1 |
Case 2 |
|
Asher |
Yen |
Asher |
Yen |
Before |
10 u - 27 |
3 u + 27 |
6.5 u + 141 |
6.5 u - 141 |
Change |
+ 27 |
- 27 |
- 141 |
+ 141 |
After |
10 u |
3 u |
6.5 u |
6.5 u |
(a)
30% =
30100 =
310 In Case 1, when Yen gives to Asher, there is an internal transfer of money from Yen to Asher. The total amount that both have remains the same.
In Case 2, when Asher gives to Yen, there is an internal transfer of money from Asher to Yen. 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 Yen and Asher have
= 10 u + 3 u
= 13 u
Amount that Yen 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 - 27 = 6.5 u + 141
10 u - 6.5 u = 141 + 27
3.5 u = 168
1 u = 168 ÷ 3.5 = 48
Amount that Asher has
= 10 u - 27
= 10 x 48 - 27
= 480 - 27
= $453
(b)
Amount that Yen has
= 3 u + 27
= 3 x 48 + 27
= 144 + 27
= $171
Answer(s): (a) $453; (b) $171