Nick and Gabriel have some money. If Nick gives $185 to Gabriel, the ratio of their money will be 2 : 5. If Nick gives $623 to Gabriel, the ratio of their money will be 1: 4. How much does Nick have?
| |
Case 1 |
Case 2 |
| |
Nick |
Gabriel |
Nick |
Gabriel |
| Before |
10 u + $185 |
25 u - $185 |
7 u + $623 |
28 u - $623 |
| Change |
- $185 |
+ $185 |
- $623 |
+ $623 |
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 + 185 = 7 u + 623
10 u - 7 u = 623 - 185
3 u = 438
1 u = 438 ÷ 3 = 146
Amount that Nick has
= 10 u + 185
= 10 x 146 + 185
= 1460 + 185
= $1645
Answer(s): $1645
