Nick and Caden have some money. If Nick gives $304 to Caden, the ratio of their money will be 2 : 5. If Nick gives $616 to Caden, the ratio of their money will be 1: 4. How much does Nick have?
| |
Case 1 |
Case 2 |
| |
Nick |
Caden |
Nick |
Caden |
| Before |
10 u + $304 |
25 u - $304 |
7 u + $616 |
28 u - $616 |
| Change |
- $304 |
+ $304 |
- $616 |
+ $616 |
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 Nick has at first is the same in both cases.
10 u + 304 = 7 u + 616
10 u - 7 u = 616 - 304
3 u = 312
1 u = 312 ÷ 3 = 104
Amount that Nick has
= 10 u + 304
= 10 x 104 + 304
= 1040 + 304
= $1344
Answer(s): $1344
