Carl and David have some money. If Carl gives $202 to David, the ratio of their money will be 2 : 5. If Carl gives $502 to David, the ratio of their money will be 1: 4. How much does Carl have?
|
Case 1 |
Case 2 |
|
Carl |
David |
Carl |
David |
Before |
10 u + $202 |
25 u - $202 |
7 u + $502 |
28 u - $502 |
Change |
- $202 |
+ $202 |
- $502 |
+ $502 |
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 + 202 = 7 u + 502
10 u - 7 u = 502 - 202
3 u = 300
1 u = 300 ÷ 3 = 100
Amount that Carl has
= 10 u + 202
= 10 x 100 + 202
= 1000 + 202
= $1202
Answer(s): $1202