Liam and Zane have some money. If Liam gives $356 to Zane, the ratio of their money will be 2 : 5. If Liam gives $497 to Zane, the ratio of their money will be 1: 4. How much does Liam have?
| |
Case 1 |
Case 2 |
| |
Liam |
Zane |
Liam |
Zane |
| Before |
10 u + $356 |
25 u - $356 |
7 u + $497 |
28 u - $497 |
| Change |
- $356 |
+ $356 |
- $497 |
+ $497 |
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 + 356 = 7 u + 497
10 u - 7 u = 497 - 356
3 u = 141
1 u = 141 ÷ 3 = 47
Amount that Liam has
= 10 u + 356
= 10 x 47 + 356
= 470 + 356
= $826
Answer(s): $826
