Liam and Tommy have some money. If Liam gives $257 to Tommy, the ratio of their money will be 2 : 5. If Liam gives $647 to Tommy, the ratio of their money will be 1: 4. How much does Liam have?
| |
Case 1 |
Case 2 |
| |
Liam |
Tommy |
Liam |
Tommy |
| Before |
10 u + $257 |
25 u - $257 |
7 u + $647 |
28 u - $647 |
| Change |
- $257 |
+ $257 |
- $647 |
+ $647 |
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 + 257 = 7 u + 647
10 u - 7 u = 647 - 257
3 u = 390
1 u = 390 ÷ 3 = 130
Amount that Liam has
= 10 u + 257
= 10 x 130 + 257
= 1300 + 257
= $1557
Answer(s): $1557
