Ivan and Archie have some money. If Ivan gives $152 to Archie, the ratio of their money will be 2 : 5. If Ivan gives $671 to Archie, the ratio of their money will be 1: 4. How much does Ivan have?
| |
Case 1 |
Case 2 |
| |
Ivan |
Archie |
Ivan |
Archie |
| Before |
10 u + $152 |
25 u - $152 |
7 u + $671 |
28 u - $671 |
| Change |
- $152 |
+ $152 |
- $671 |
+ $671 |
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 + 152 = 7 u + 671
10 u - 7 u = 671 - 152
3 u = 519
1 u = 519 ÷ 3 = 173
Amount that Ivan has
= 10 u + 152
= 10 x 173 + 152
= 1730 + 152
= $1882
Answer(s): $1882
