Caden and Mark have some money. If Caden gives $162 to Mark, the ratio of their money will be 2 : 5. If Caden gives $660 to Mark, the ratio of their money will be 1: 4. How much does Caden have?
| |
Case 1 |
Case 2 |
| |
Caden |
Mark |
Caden |
Mark |
| Before |
10 u + $162 |
25 u - $162 |
7 u + $660 |
28 u - $660 |
| Change |
- $162 |
+ $162 |
- $660 |
+ $660 |
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 Caden has at first is the same in both cases.
10 u + 162 = 7 u + 660
10 u - 7 u = 660 - 162
3 u = 498
1 u = 498 ÷ 3 = 166
Amount that Caden has
= 10 u + 162
= 10 x 166 + 162
= 1660 + 162
= $1822
Answer(s): $1822
