Liam and Ken have some money. If Liam gives $332 to Ken, the ratio of their money will be 2 : 5. If Liam gives $470 to Ken, the ratio of their money will be 1: 4. How much does Liam have?
| |
Case 1 |
Case 2 |
| |
Liam |
Ken |
Liam |
Ken |
| Before |
10 u + $332 |
25 u - $332 |
7 u + $470 |
28 u - $470 |
| Change |
- $332 |
+ $332 |
- $470 |
+ $470 |
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 + 332 = 7 u + 470
10 u - 7 u = 470 - 332
3 u = 138
1 u = 138 ÷ 3 = 46
Amount that Liam has
= 10 u + 332
= 10 x 46 + 332
= 460 + 332
= $792
Answer(s): $792
