Ben and Jenson have some money. If Ben gives $123 to Jenson, the ratio of their money will be 2 : 5. If Ben gives $579 to Jenson, the ratio of their money will be 1: 4. How much does Ben have?
| |
Case 1 |
Case 2 |
| |
Ben |
Jenson |
Ben |
Jenson |
| Before |
10 u + $123 |
25 u - $123 |
7 u + $579 |
28 u - $579 |
| Change |
- $123 |
+ $123 |
- $579 |
+ $579 |
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 + 123 = 7 u + 579
10 u - 7 u = 579 - 123
3 u = 456
1 u = 456 ÷ 3 = 152
Amount that Ben has
= 10 u + 123
= 10 x 152 + 123
= 1520 + 123
= $1643
Answer(s): $1643
