Ivan and Jeremy have some money. If Ivan gives $259 to Jeremy, the ratio of their money will be 3 : 5. If Ivan gives $616 to Jeremy, the ratio of their money will be 1: 4. How much does Ivan have?
| |
Case 1 |
Case 2 |
| |
Ivan |
Jeremy |
Ivan |
Jeremy |
| Before |
15 u + $259 |
25 u - $259 |
8 u + $616 |
32 u - $616 |
| Change |
- $259 |
+ $259 |
- $616 |
+ $616 |
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 + 259 = 8 u + 616
15 u - 8 u = 616 - 259
7 u = 357
1 u = 357 ÷ 7 = 51
Amount that Ivan has
= 15 u + 259
= 15 x 51 + 259
= 765 + 259
= $1024
Answer(s): $1024
