Ivan and Perry have some money. If Ivan gives $354 to Perry, the ratio of their money will be 2 : 5. If Ivan gives $516 to Perry, the ratio of their money will be 1: 4. How much does Ivan have?
|
Case 1 |
Case 2 |
|
Ivan |
Perry |
Ivan |
Perry |
Before |
10 u + $354 |
25 u - $354 |
7 u + $516 |
28 u - $516 |
Change |
- $354 |
+ $354 |
- $516 |
+ $516 |
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 + 354 = 7 u + 516
10 u - 7 u = 516 - 354
3 u = 162
1 u = 162 ÷ 3 = 54
Amount that Ivan has
= 10 u + 354
= 10 x 54 + 354
= 540 + 354
= $894
Answer(s): $894