Asher and Japheth have some money. If Asher gives $229 to Japheth, the ratio of their money will be 3 : 5. If Asher gives $523 to Japheth, the ratio of their money will be 1: 4. How much does Asher have?
| |
Case 1 |
Case 2 |
| |
Asher |
Japheth |
Asher |
Japheth |
| Before |
15 u + $229 |
25 u - $229 |
8 u + $523 |
32 u - $523 |
| Change |
- $229 |
+ $229 |
- $523 |
+ $523 |
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 Asher has at first is the same in both cases.
15 u + 229 = 8 u + 523
15 u - 8 u = 523 - 229
7 u = 294
1 u = 294 ÷ 7 = 42
Amount that Asher has
= 15 u + 229
= 15 x 42 + 229
= 630 + 229
= $859
Answer(s): $859
