Zeph and Ken have some money. If Zeph gives $250 to Ken, the ratio of their money will be 2 : 5. If Zeph gives $577 to Ken, the ratio of their money will be 1: 4. How much does Zeph have?
| |
Case 1 |
Case 2 |
| |
Zeph |
Ken |
Zeph |
Ken |
| Before |
10 u + $250 |
25 u - $250 |
7 u + $577 |
28 u - $577 |
| Change |
- $250 |
+ $250 |
- $577 |
+ $577 |
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 Zeph has at first is the same in both cases.
10 u + 250 = 7 u + 577
10 u - 7 u = 577 - 250
3 u = 327
1 u = 327 ÷ 3 = 109
Amount that Zeph has
= 10 u + 250
= 10 x 109 + 250
= 1090 + 250
= $1340
Answer(s): $1340
