Ivan and Ethan have some money. If Ivan gives $400 to Ethan, the ratio of their money will be 2 : 5. If Ivan gives $643 to Ethan, the ratio of their money will be 1: 4. How much does Ivan have?
| |
Case 1 |
Case 2 |
| |
Ivan |
Ethan |
Ivan |
Ethan |
| Before |
10 u + $400 |
25 u - $400 |
7 u + $643 |
28 u - $643 |
| Change |
- $400 |
+ $400 |
- $643 |
+ $643 |
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 + 400 = 7 u + 643
10 u - 7 u = 643 - 400
3 u = 243
1 u = 243 ÷ 3 = 81
Amount that Ivan has
= 10 u + 400
= 10 x 81 + 400
= 810 + 400
= $1210
Answer(s): $1210
