Nick and Jack have some money. If Nick gives $367 to Jack, the ratio of their money will be 3 : 5. If Nick gives $542 to Jack, the ratio of their money will be 1: 4. How much does Nick have?
| |
Case 1 |
Case 2 |
| |
Nick |
Jack |
Nick |
Jack |
| Before |
15 u + $367 |
25 u - $367 |
8 u + $542 |
32 u - $542 |
| Change |
- $367 |
+ $367 |
- $542 |
+ $542 |
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 Nick has at first is the same in both cases.
15 u + 367 = 8 u + 542
15 u - 8 u = 542 - 367
7 u = 175
1 u = 175 ÷ 7 = 25
Amount that Nick has
= 15 u + 367
= 15 x 25 + 367
= 375 + 367
= $742
Answer(s): $742
