If Yen gives Ethan $16, the amount of money she has will be 30% of his. If Ethan gives Yen $145, he will have the same amount of money as her. How much money did each of them have?
(a) Ethan
(b) Yen
|
Case 1 |
Case 2 |
|
Ethan |
Yen |
Ethan |
Yen |
Before |
10 u - 16 |
3 u + 16 |
6.5 u + 145 |
6.5 u - 145 |
Change |
+ 16 |
- 16 |
- 145 |
+ 145 |
After |
10 u |
3 u |
6.5 u |
6.5 u |
(a)
30% =
30100 =
310 In Case 1, when Yen gives to Ethan, there is an internal transfer of money from Yen to Ethan. The total amount that both have remains the same.
In Case 2, when Ethan gives to Yen, there is an internal transfer of money from Ethan 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 Ethan have
= 10 u + 3 u
= 13 u
Amount that Yen and Ethan each has in the end for Case 2
= 13 u ÷ 2
= 6.5 u
Amount that Ethan has at first is the same in Case 1 and Case 2.
10 u - 16 = 6.5 u + 145
10 u - 6.5 u = 145 + 16
3.5 u = 161
1 u = 161 ÷ 3.5 = 46
Amount that Ethan has
= 10 u - 16
= 10 x 46 - 16
= 460 - 16
= $444
(b)
Amount that Yen has
= 3 u + 16
= 3 x 46 + 16
= 138 + 16
= $154
Answer(s): (a) $444; (b) $154