Cody and Tim have some money. If Cody gives $321 to Tim, the ratio of their money will be 3 : 5. If Cody gives $559 to Tim, the ratio of their money will be 1: 4. How much does Cody have?
| |
Case 1 |
Case 2 |
| |
Cody |
Tim |
Cody |
Tim |
| Before |
15 u + $321 |
25 u - $321 |
8 u + $559 |
32 u - $559 |
| Change |
- $321 |
+ $321 |
- $559 |
+ $559 |
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 Cody has at first is the same in both cases.
15 u + 321 = 8 u + 559
15 u - 8 u = 559 - 321
7 u = 238
1 u = 238 ÷ 7 = 34
Amount that Cody has
= 15 u + 321
= 15 x 34 + 321
= 510 + 321
= $831
Answer(s): $831
