Caden and Oscar have some money. If Caden gives $195 to Oscar, the ratio of their money will be 3 : 5. If Caden gives $510 to Oscar, the ratio of their money will be 1: 4. How much does Caden have?
| |
Case 1 |
Case 2 |
| |
Caden |
Oscar |
Caden |
Oscar |
| Before |
15 u + $195 |
25 u - $195 |
8 u + $510 |
32 u - $510 |
| Change |
- $195 |
+ $195 |
- $510 |
+ $510 |
After
|
3x5 =
15 u |
5x5 =
25 u |
1x8 =
8 u |
4x8 =
32 u |
The total amounts in both cases remain unchanged. Make the total amounts in both cases the same. LCM of 8 and 5 is 40.
The amount that Caden has at first is the same in both cases.
15 u + 195 = 8 u + 510
15 u - 8 u = 510 - 195
7 u = 315
1 u = 315 ÷ 7 = 45
Amount that Caden has
= 15 u + 195
= 15 x 45 + 195
= 675 + 195
= $870
Answer(s): $870
