Ken and Gabriel have some money. If Ken gives $366 to Gabriel, the ratio of their money will be 2 : 5. If Ken gives $573 to Gabriel, the ratio of their money will be 1: 4. How much does Ken have?
| |
Case 1 |
Case 2 |
| |
Ken |
Gabriel |
Ken |
Gabriel |
| Before |
10 u + $366 |
25 u - $366 |
7 u + $573 |
28 u - $573 |
| Change |
- $366 |
+ $366 |
- $573 |
+ $573 |
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 Ken has at first is the same in both cases.
10 u + 366 = 7 u + 573
10 u - 7 u = 573 - 366
3 u = 207
1 u = 207 ÷ 3 = 69
Amount that Ken has
= 10 u + 366
= 10 x 69 + 366
= 690 + 366
= $1056
Answer(s): $1056
