If Yen gives Ken $38, the amount of money she has will be 30% of his. If Ken gives Yen $74, he will have the same amount of money as her. How much money did each of them have?
(a) Ken
(b) Yen
|
Case 1 |
Case 2 |
|
Ken |
Yen |
Ken |
Yen |
Before |
10 u - 38 |
3 u + 38 |
6.5 u + 74 |
6.5 u - 74 |
Change |
+ 38 |
- 38 |
- 74 |
+ 74 |
After |
10 u |
3 u |
6.5 u |
6.5 u |
(a)
30% =
30100 =
310 In Case 1, when Yen gives to Ken, there is an internal transfer of money from Yen to Ken. The total amount that both have remains the same.
In Case 2, when Ken gives to Yen, there is an internal transfer of money from Ken 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 Ken have
= 10 u + 3 u
= 13 u
Amount that Yen and Ken each has in the end for Case 2
= 13 u ÷ 2
= 6.5 u
Amount that Ken has at first is the same in Case 1 and Case 2.
10 u - 38 = 6.5 u + 74
10 u - 6.5 u = 74 + 38
3.5 u = 112
1 u = 112 ÷ 3.5 = 32
Amount that Ken has
= 10 u - 38
= 10 x 32 - 38
= 320 - 38
= $282
(b)
Amount that Yen has
= 3 u + 38
= 3 x 32 + 38
= 96 + 38
= $134
Answer(s): (a) $282; (b) $134