Valen and Jenson have some money. If Valen gives $320 to Jenson, the ratio of their money will be 2 : 5. If Valen gives $497 to Jenson, the ratio of their money will be 1: 4. How much does Valen have?
| |
Case 1 |
Case 2 |
| |
Valen |
Jenson |
Valen |
Jenson |
| Before |
10 u + $320 |
25 u - $320 |
7 u + $497 |
28 u - $497 |
| Change |
- $320 |
+ $320 |
- $497 |
+ $497 |
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 Valen has at first is the same in both cases.
10 u + 320 = 7 u + 497
10 u - 7 u = 497 - 320
3 u = 177
1 u = 177 ÷ 3 = 59
Amount that Valen has
= 10 u + 320
= 10 x 59 + 320
= 590 + 320
= $910
Answer(s): $910
