John and Seth have some money. If John gives $207 to Seth, the ratio of their money will be 2 : 5. If John gives $570 to Seth, the ratio of their money will be 1: 4. How much does John have?
|
Case 1 |
Case 2 |
|
John |
Seth |
John |
Seth |
Before |
10 u + $207 |
25 u - $207 |
7 u + $570 |
28 u - $570 |
Change |
- $207 |
+ $207 |
- $570 |
+ $570 |
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 John has at first is the same in both cases.
10 u + 207 = 7 u + 570
10 u - 7 u = 570 - 207
3 u = 363
1 u = 363 ÷ 3 = 121
Amount that John has
= 10 u + 207
= 10 x 121 + 207
= 1210 + 207
= $1417
Answer(s): $1417