Japheth and Henry have some money. If Japheth gives $163 to Henry, the ratio of their money will be 2 : 5. If Japheth gives $472 to Henry, the ratio of their money will be 1: 4. How much does Japheth have?
|
Case 1 |
Case 2 |
|
Japheth |
Henry |
Japheth |
Henry |
Before |
10 u + $163 |
25 u - $163 |
7 u + $472 |
28 u - $472 |
Change |
- $163 |
+ $163 |
- $472 |
+ $472 |
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 + 163 = 7 u + 472
10 u - 7 u = 472 - 163
3 u = 309
1 u = 309 ÷ 3 = 103
Amount that Japheth has
= 10 u + 163
= 10 x 103 + 163
= 1030 + 163
= $1193
Answer(s): $1193