Ivan and Peter have some money. If Ivan gives $378 to Peter, the ratio of their money will be 3 : 5. If Ivan gives $455 to Peter, the ratio of their money will be 1: 4. How much does Ivan have?
| |
Case 1 |
Case 2 |
| |
Ivan |
Peter |
Ivan |
Peter |
| Before |
15 u + $378 |
25 u - $378 |
8 u + $455 |
32 u - $455 |
| Change |
- $378 |
+ $378 |
- $455 |
+ $455 |
After
|
3x5 =
15 u |
5x5 =
25 u |
1x8 =
8 u |
4x8 =
32 u |
The total amounts in both cases remain unchanged. Make the total amounts in both cases the same. LCM of 8 and 5 is 40.
The amount that Ivan has at first is the same in both cases.
15 u + 378 = 8 u + 455
15 u - 8 u = 455 - 378
7 u = 77
1 u = 77 ÷ 7 = 11
Amount that Ivan has
= 15 u + 378
= 15 x 11 + 378
= 165 + 378
= $543
Answer(s): $543
