Carl and Caden have some money. If Carl gives $367 to Caden, the ratio of their money will be 2 : 5. If Carl gives $562 to Caden, the ratio of their money will be 1: 4. How much does Carl have?
| |
Case 1 |
Case 2 |
| |
Carl |
Caden |
Carl |
Caden |
| Before |
10 u + $367 |
25 u - $367 |
7 u + $562 |
28 u - $562 |
| Change |
- $367 |
+ $367 |
- $562 |
+ $562 |
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 Carl has at first is the same in both cases.
10 u + 367 = 7 u + 562
10 u - 7 u = 562 - 367
3 u = 195
1 u = 195 ÷ 3 = 65
Amount that Carl has
= 10 u + 367
= 10 x 65 + 367
= 650 + 367
= $1017
Answer(s): $1017
