Andy and Zeph have some money. If Andy gives $154 to Zeph, the ratio of their money will be 2 : 5. If Andy gives $514 to Zeph, the ratio of their money will be 1: 4. How much does Andy have?
| |
Case 1 |
Case 2 |
| |
Andy |
Zeph |
Andy |
Zeph |
| Before |
10 u + $154 |
25 u - $154 |
7 u + $514 |
28 u - $514 |
| Change |
- $154 |
+ $154 |
- $514 |
+ $514 |
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 Andy has at first is the same in both cases.
10 u + 154 = 7 u + 514
10 u - 7 u = 514 - 154
3 u = 360
1 u = 360 ÷ 3 = 120
Amount that Andy has
= 10 u + 154
= 10 x 120 + 154
= 1200 + 154
= $1354
Answer(s): $1354
