Eric and Japheth have some money. If Eric gives $327 to Japheth, the ratio of their money will be 2 : 5. If Eric gives $633 to Japheth, the ratio of their money will be 1: 4. How much does Eric have?
| |
Case 1 |
Case 2 |
| |
Eric |
Japheth |
Eric |
Japheth |
| Before |
10 u + $327 |
25 u - $327 |
7 u + $633 |
28 u - $633 |
| Change |
- $327 |
+ $327 |
- $633 |
+ $633 |
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 Eric has at first is the same in both cases.
10 u + 327 = 7 u + 633
10 u - 7 u = 633 - 327
3 u = 306
1 u = 306 ÷ 3 = 102
Amount that Eric has
= 10 u + 327
= 10 x 102 + 327
= 1020 + 327
= $1347
Answer(s): $1347
