Zeph and Paul have some money. If Zeph gives $171 to Paul, the ratio of their money will be 2 : 5. If Zeph gives $480 to Paul, the ratio of their money will be 1: 4. How much does Zeph have?
| |
Case 1 |
Case 2 |
| |
Zeph |
Paul |
Zeph |
Paul |
| Before |
10 u + $171 |
25 u - $171 |
7 u + $480 |
28 u - $480 |
| Change |
- $171 |
+ $171 |
- $480 |
+ $480 |
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 + 171 = 7 u + 480
10 u - 7 u = 480 - 171
3 u = 309
1 u = 309 ÷ 3 = 103
Amount that Zeph has
= 10 u + 171
= 10 x 103 + 171
= 1030 + 171
= $1201
Answer(s): $1201
