Reggie and Bryan have some money. If Reggie gives $157 to Bryan, the ratio of their money will be 2 : 5. If Reggie gives $472 to Bryan, the ratio of their money will be 1: 4. How much does Reggie have?
| |
Case 1 |
Case 2 |
| |
Reggie |
Bryan |
Reggie |
Bryan |
| Before |
10 u + $157 |
25 u - $157 |
7 u + $472 |
28 u - $472 |
| Change |
- $157 |
+ $157 |
- $472 |
+ $472 |
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 Reggie has at first is the same in both cases.
10 u + 157 = 7 u + 472
10 u - 7 u = 472 - 157
3 u = 315
1 u = 315 ÷ 3 = 105
Amount that Reggie has
= 10 u + 157
= 10 x 105 + 157
= 1050 + 157
= $1207
Answer(s): $1207
