Valen and Caden have some money. If Valen gives $233 to Caden, the ratio of their money will be 2 : 5. If Valen gives $671 to Caden, the ratio of their money will be 1: 4. How much does Valen have?
| |
Case 1 |
Case 2 |
| |
Valen |
Caden |
Valen |
Caden |
| Before |
10 u + $233 |
25 u - $233 |
7 u + $671 |
28 u - $671 |
| Change |
- $233 |
+ $233 |
- $671 |
+ $671 |
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 + 233 = 7 u + 671
10 u - 7 u = 671 - 233
3 u = 438
1 u = 438 ÷ 3 = 146
Amount that Valen has
= 10 u + 233
= 10 x 146 + 233
= 1460 + 233
= $1693
Answer(s): $1693
