Jeremy and Billy have some money. If Jeremy gives $159 to Billy, the ratio of their money will be 2 : 5. If Jeremy gives $582 to Billy, the ratio of their money will be 1: 4. How much does Jeremy have?
| |
Case 1 |
Case 2 |
| |
Jeremy |
Billy |
Jeremy |
Billy |
| Before |
10 u + $159 |
25 u - $159 |
7 u + $582 |
28 u - $582 |
| Change |
- $159 |
+ $159 |
- $582 |
+ $582 |
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 Jeremy has at first is the same in both cases.
10 u + 159 = 7 u + 582
10 u - 7 u = 582 - 159
3 u = 423
1 u = 423 ÷ 3 = 141
Amount that Jeremy has
= 10 u + 159
= 10 x 141 + 159
= 1410 + 159
= $1569
Answer(s): $1569
