Peter and Wesley have some money. If Peter gives $131 to Wesley, the ratio of their money will be 3 : 5. If Peter gives $670 to Wesley, the ratio of their money will be 1: 4. How much does Peter have?
| |
Case 1 |
Case 2 |
| |
Peter |
Wesley |
Peter |
Wesley |
| Before |
15 u + $131 |
25 u - $131 |
8 u + $670 |
32 u - $670 |
| Change |
- $131 |
+ $131 |
- $670 |
+ $670 |
After
|
3x5 =
15 u |
5x5 =
25 u |
1x8 =
8 u |
4x8 =
32 u |
The total amounts in both cases remain unchanged. Make the total amounts in both cases the same. LCM of 8 and 5 is 40.
The amount that Peter has at first is the same in both cases.
15 u + 131 = 8 u + 670
15 u - 8 u = 670 - 131
7 u = 539
1 u = 539 ÷ 7 = 77
Amount that Peter has
= 15 u + 131
= 15 x 77 + 131
= 1155 + 131
= $1286
Answer(s): $1286
