Japheth and David have some money. If Japheth gives $200 to David, the ratio of their money will be 3 : 5. If Japheth gives $669 to David, the ratio of their money will be 1: 4. How much does Japheth have?
| |
Case 1 |
Case 2 |
| |
Japheth |
David |
Japheth |
David |
| Before |
15 u + $200 |
25 u - $200 |
8 u + $669 |
32 u - $669 |
| Change |
- $200 |
+ $200 |
- $669 |
+ $669 |
After
|
3x5 =
15 u |
5x5 =
25 u |
1x8 =
8 u |
4x8 =
32 u |
The total amounts in both cases remain unchanged. Make the total amounts in both cases the same. LCM of 8 and 5 is 40.
The amount that Japheth has at first is the same in both cases.
15 u + 200 = 8 u + 669
15 u - 8 u = 669 - 200
7 u = 469
1 u = 469 ÷ 7 = 67
Amount that Japheth has
= 15 u + 200
= 15 x 67 + 200
= 1005 + 200
= $1205
Answer(s): $1205
