Ivan and Seth have some money. If Ivan gives $201 to Seth, the ratio of their money will be 2 : 5. If Ivan gives $585 to Seth, the ratio of their money will be 1: 4. How much does Ivan have?
|
Case 1 |
Case 2 |
|
Ivan |
Seth |
Ivan |
Seth |
Before |
10 u + $201 |
25 u - $201 |
7 u + $585 |
28 u - $585 |
Change |
- $201 |
+ $201 |
- $585 |
+ $585 |
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 Ivan has at first is the same in both cases.
10 u + 201 = 7 u + 585
10 u - 7 u = 585 - 201
3 u = 384
1 u = 384 ÷ 3 = 128
Amount that Ivan has
= 10 u + 201
= 10 x 128 + 201
= 1280 + 201
= $1481
Answer(s): $1481