John and Nick have some money. If John gives $352 to Nick, the ratio of their money will be 3 : 5. If John gives $667 to Nick, the ratio of their money will be 1: 4. How much does John have?
| |
Case 1 |
Case 2 |
| |
John |
Nick |
John |
Nick |
| Before |
15 u + $352 |
25 u - $352 |
8 u + $667 |
32 u - $667 |
| Change |
- $352 |
+ $352 |
- $667 |
+ $667 |
After
|
3x5 =
15 u |
5x5 =
25 u |
1x8 =
8 u |
4x8 =
32 u |
The total amounts in both cases remain unchanged. Make the total amounts in both cases the same. LCM of 8 and 5 is 40.
The amount that John has at first is the same in both cases.
15 u + 352 = 8 u + 667
15 u - 8 u = 667 - 352
7 u = 315
1 u = 315 ÷ 7 = 45
Amount that John has
= 15 u + 352
= 15 x 45 + 352
= 675 + 352
= $1027
Answer(s): $1027
