John and Charlie have some money. If John gives $279 to Charlie, the ratio of their money will be 2 : 5. If John gives $657 to Charlie, the ratio of their money will be 1: 4. How much does John have?
|
Case 1 |
Case 2 |
|
John |
Charlie |
John |
Charlie |
Before |
10 u + $279 |
25 u - $279 |
7 u + $657 |
28 u - $657 |
Change |
- $279 |
+ $279 |
- $657 |
+ $657 |
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 + 279 = 7 u + 657
10 u - 7 u = 657 - 279
3 u = 378
1 u = 378 ÷ 3 = 126
Amount that John has
= 10 u + 279
= 10 x 126 + 279
= 1260 + 279
= $1539
Answer(s): $1539