Liam and Bryan have some money. If Liam gives $293 to Bryan, the ratio of their money will be 2 : 5. If Liam gives $686 to Bryan, the ratio of their money will be 1: 4. How much does Liam have?
| |
Case 1 |
Case 2 |
| |
Liam |
Bryan |
Liam |
Bryan |
| Before |
10 u + $293 |
25 u - $293 |
7 u + $686 |
28 u - $686 |
| Change |
- $293 |
+ $293 |
- $686 |
+ $686 |
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 Liam has at first is the same in both cases.
10 u + 293 = 7 u + 686
10 u - 7 u = 686 - 293
3 u = 393
1 u = 393 ÷ 3 = 131
Amount that Liam has
= 10 u + 293
= 10 x 131 + 293
= 1310 + 293
= $1603
Answer(s): $1603
