Japheth and Valen have some money. If Japheth gives $338 to Valen, the ratio of their money will be 2 : 5. If Japheth gives $539 to Valen, the ratio of their money will be 1: 4. How much does Japheth have?
| |
Case 1 |
Case 2 |
| |
Japheth |
Valen |
Japheth |
Valen |
| Before |
10 u + $338 |
25 u - $338 |
7 u + $539 |
28 u - $539 |
| Change |
- $338 |
+ $338 |
- $539 |
+ $539 |
After
|
2x5 =
10 u |
5x5 =
25 u |
1x7 =
7 u |
4x7 =
28 u |
The total amounts in both cases remain unchanged. Make the total amounts in both cases the same. LCM of 7 and 5 is 35.
The amount that Japheth has at first is the same in both cases.
10 u + 338 = 7 u + 539
10 u - 7 u = 539 - 338
3 u = 201
1 u = 201 ÷ 3 = 67
Amount that Japheth has
= 10 u + 338
= 10 x 67 + 338
= 670 + 338
= $1008
Answer(s): $1008
