Ben and Japheth have some money. If Ben gives $284 to Japheth, the ratio of their money will be 2 : 5. If Ben gives $698 to Japheth, the ratio of their money will be 1: 4. How much does Ben have?
|
Case 1 |
Case 2 |
|
Ben |
Japheth |
Ben |
Japheth |
Before |
10 u + $284 |
25 u - $284 |
7 u + $698 |
28 u - $698 |
Change |
- $284 |
+ $284 |
- $698 |
+ $698 |
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 Ben has at first is the same in both cases.
10 u + 284 = 7 u + 698
10 u - 7 u = 698 - 284
3 u = 414
1 u = 414 ÷ 3 = 138
Amount that Ben has
= 10 u + 284
= 10 x 138 + 284
= 1380 + 284
= $1664
Answer(s): $1664